Sharp EL 5230 User Manual
®
EL-5230  
EL-5250  
PROGRAMMABLE SCIENTIFIC  
CALCULATOR  
OPERATION MANUAL  
SHARP EL-5230/5250  
Programmable Scientific Calculator  
Introduction  
Chapter 1:  
BeforeYou Get Started  
Chapter 2:  
General Information  
Chapter 3:  
Scientific Calculations  
Chapter 4:  
Statistical Calculations  
Chapter 5:  
Equation Solvers  
Chapter 6:  
Complex Number Calculations  
Chapter 7:  
Programming  
Chapter 8:  
Application Examples  
Appendix  
1
Contents  
Introduction ...........................................................7  
Operational Notes .................................................................................... 8  
Key Notation in This Manual .................................................................... 9  
Chapter 1: BeforeYou Get Started.....................11  
Preparing to Use the Calculator ............................................................ 11  
Resetting the calculator ................................................................. 11  
The Hard Case....................................................................................... 12  
Calculator Layout and Display Symbols ................................................ 13  
Operating Modes ................................................................................... 15  
Selecting a mode ........................................................................... 15  
What you can do in each mode ..................................................... 15  
A Quick Tour ........................................................................................... 16  
Turning the calculator on and off ................................................... 16  
Entering and solving an expression............................................... 16  
Editing an expression ..................................................................... 17  
Using variables ............................................................................... 18  
Using simulation calculations (ALGB) ........................................... 19  
Using the solver function................................................................ 21  
Other features ................................................................................ 22  
Chapter 2: General Information .........................23  
Clearing the Entry and Memories.......................................................... 23  
Memory clear key ........................................................................... 23  
Editing and Correcting an Equation ...................................................... 24  
Cursor keys .................................................................................... 24  
Overwrite mode and insert mode .................................................. 24  
Delete key....................................................................................... 25  
Multi-entry recall function ............................................................... 25  
The SET UP menu ................................................................................. 26  
Determination of the angular unit .................................................. 26  
Selecting the display notation and number of decimal places ...... 26  
2
Contents  
Setting the floating point numbers system in scientific notation ... 26  
Using Memories ..................................................................................... 27  
Using alphabetic characters .......................................................... 27  
Using global variables .................................................................... 27  
Using local variables ...................................................................... 28  
Using variables in an equation or a program................................. 29  
Using the last answer memory ...................................................... 30  
Global variable M ........................................................................... 30  
Using memory in each mode ......................................................... 31  
Resetting the calculator ................................................................. 32  
Chapter 3: Scientific Calculations .....................33  
NORMAL mode...................................................................................... 33  
Arithmetic operations ..................................................................... 33  
Constant calculations ..................................................................... 34  
Functions................................................................................................ 34  
Math menu Functions ............................................................................ 36  
Differential/Integral Functions ................................................................ 38  
Differential function ........................................................................ 38  
Integral function .............................................................................. 39  
When performing integral calculations .......................................... 40  
Random Function .................................................................................. 41  
Random numbers ........................................................................... 41  
Random dice .................................................................................. 41  
Random coin .................................................................................. 41  
Random integer.............................................................................. 41  
Angular Unit Conversions ...................................................................... 42  
Chain Calculations ................................................................................. 42  
Fraction Calculations ............................................................................. 43  
Binary, Pental, Octal, Decimal and Hexadecimal Operations (N-base) ... 44  
Time, Decimal and Sexagesimal Calculations ...................................... 46  
Coordinate Conversions ........................................................................ 47  
Calculations Using Physical Constants ................................................. 48  
Calculations Using Engineering Prefixes .............................................. 50  
Modify Function...................................................................................... 51  
3
Contents  
Solver Function ...................................................................................... 52  
Entering and solving an equation .................................................. 52  
Changing the value of variables and editing an equation ............. 52  
Solving an equation ....................................................................... 53  
Important notes .............................................................................. 54  
Simulation Calculation (ALGB) .............................................................. 55  
Entering an expression for simulation calculation ......................... 55  
Changing a value of variables and editing an expression ............. 55  
Simulate an equation for different values ...................................... 56  
Filing Equations ..................................................................................... 58  
Saving an equation ........................................................................ 58  
Loading and deleting an equation ................................................. 59  
Chapter 4: Statistical Calculations ....................61  
Single-variable statistical calculation ............................................. 62  
Linear regression calculation ......................................................... 62  
Exponential regression, logarithmic regression,  
power regression, and inverse regression calculation .................. 62  
Quadratic regression calculation ................................................... 63  
Data Entry and Correction ..................................................................... 63  
Data entry ....................................................................................... 63  
Data correction ............................................................................... 63  
Statistical Calculation Formulas ............................................................ 65  
Normal Probability Calculations ............................................................ 66  
Statistical Calculations Examples ......................................................... 67  
Chapter 5: Equation Solvers ..............................69  
Simultaneous Linear Equations............................................................. 69  
Quadratic and Cubic Equation Solvers ................................................. 71  
Chapter 6: Complex Number Calculations .......73  
Complex Number Entry ......................................................................... 73  
Chapter 7: Programming ....................................75  
PROG mode........................................................................................... 75  
4
Contents  
Entering the PROG mode .............................................................. 75  
Selecting the NORMAL program mode or the NBASE  
program mode ................................................................................ 75  
Programming concept .................................................................... 75  
Keys and display ............................................................................ 76  
Creating a NEW Program ...................................................................... 76  
Creating a NEW program ............................................................... 76  
Use of variables.............................................................................. 77  
Programming Commands ...................................................................... 79  
Input and display commands ......................................................... 79  
Flow control .................................................................................... 81  
Equalities and inequalities ............................................................. 82  
Statistical Commands ............................................................................ 83  
Editing a Program .................................................................................. 84  
Error Messages...................................................................................... 85  
Deleting Programs ................................................................................. 86  
Chapter 8: Application Examples ......................87  
Programming Examples ........................................................................ 87  
Some like it hot (Celsius-Fahrenheit conversion) .......................... 87  
The Heron Formula ........................................................................ 89  
2B or not 2B (N-base conversion) ................................................. 91  
T test............................................................................................... 93  
A circle that passes through 3 points ............................................ 95  
Radioactive decay .......................................................................... 97  
Delta-Y impedance circuit transformation ..................................... 99  
Obtaining tensions of strings ....................................................... 102  
Purchasing with payment in n-month installments ...................... 104  
Digital dice .................................................................................... 106  
How many digits can you remember? ......................................... 107  
Calculation Examples .......................................................................... 110  
Geosynchronous orbits ................................................................ 110  
Twinkle, twinkle, little star (Apparent magnitude of stars) ........... 111  
Memory calculations .................................................................... 113  
The state lottery ........................................................................... 114  
5
Contents  
Appendix............................................................115  
Battery Replacement ........................................................................... 115  
Batteries used .............................................................................. 115  
Notes on battery replacement ..................................................... 115  
When to replace the batteries ...................................................... 115  
Cautions ....................................................................................... 116  
Replacement procedure ............................................................... 116  
Automatic power off function........................................................ 117  
The OPTION menu .............................................................................. 118  
The OPTION display .................................................................... 118  
Contrast ........................................................................................ 118  
Memory check .............................................................................. 118  
Deleting equation files and programs .......................................... 119  
If an Abnormal Condition Occurs ........................................................ 119  
Error Messages.................................................................................... 120  
Using the Solver Function Effectively .................................................. 121  
Newton’s method .......................................................................... 121  
‘Dead end’ approximations ........................................................... 121  
Range of expected values............................................................ 121  
Calculation accuracy .................................................................... 122  
Changing the range of expected values ...................................... 122  
Equations that are difficult to solve .............................................. 123  
Technical Data ..................................................................................... 124  
Calculation ranges ....................................................................... 124  
Memory usage ............................................................................. 126  
Priority levels in calculations ........................................................ 127  
Specifications ....................................................................................... 128  
For More Information about Scientific Calculators .............................. 129  
6
Introduction  
Thank you for purchasing the SHARP Programmable Scientific Calculator  
Model EL-5230/5250.  
After reading this manual, store it in a convenient location for future reference.  
• Unless the model is specified, all text and other material appearing in this  
manual applies to both models (EL-5230 and EL-5250).  
• Either of the models described in this manual may not be available in  
some countries.  
• Screen examples shown in this manual may not look exactly the same as  
what is seen on the product. For instance, screen examples will show only  
the symbols necessary for explanation of each particular calculation.  
• All company and/or product names are trademarks and/or registered  
trademarks of their respective holders.  
7
Introduction  
Operational Notes  
• Do not carry the calculator around in your back pocket, as it may break  
when you sit down. The display is made of glass and is particularly fragile.  
• Keep the calculator away from extreme heat such as on a car dashboard  
or near a heater, and avoid exposing it to excessively humid or dusty  
environments.  
• Since this product is not waterproof, do not use it or store it where fluids,  
for example water, can splash onto it. Raindrops, water spray, juice, coffee,  
steam, perspiration, etc. will also cause malfunction.  
• Clean with a soft, dry cloth. Do not use solvents or a wet cloth.  
• Do not drop it or apply excessive force.  
• Never dispose of batteries in a fire.  
• Keep batteries out of the reach of children.  
• This product, including accessories, may change due to upgrading without  
prior notice.  
NOTICE  
•
•
SHARP strongly recommends that separate permanent written  
records be kept of all important data. Data may be lost or altered in  
virtually any electronic memory product under certain circum-  
stances. Therefore, SHARP assumes no responsibility for data lost  
or otherwise rendered unusable whether as a result of improper use,  
repairs, defects, battery replacement, use after the specified battery  
life has expired, or any other cause.  
SHARP will not be liable nor responsible for any incidental or  
consequential economic or property damage caused by misuse and/  
or malfunctions of this product and its peripherals, unless such  
liability is acknowledged by law.  
8
Introduction  
Key Notation in This Manual  
In this manual, key operations are described as follows:  
To specify ex : @ "..................... ቢ  
To specify In : i  
To specify F : ; F ........................... ባ  
To specify d/c : @ F..................... ቢ  
b
To specify a / : k  
c
To specify H : ; H........................... ባ  
To specify i : Q .............................. ቤ  
ቢ Functions that are printed in orange above the key require @ to be  
pressed first before the key.  
ባ When you specify the memory (printed in blue above the key), press  
; first.  
Alpha-numeric characters for input are not shown as keys but as regular  
alpha-numeric characters.  
ቤ Functions that are printed in grey (gray) adjacent to the keys are effective  
in specific modes.  
Note:  
• To make the cursor easier to see in diagrams throughout the manual,  
it is depicted as ‘_’ under the character though it may actually appear  
as a rectangular cursor on the display.  
Example  
Press j @ s ; R  
A k S 10  
• @ s and ; R means you have  
NORMAL MODE  
πRŒ˚–10_  
to press @ followed by ` key and  
0.  
; followed by 5 key.  
9
10  
Chapter 1  
Before You Get Started  
Preparing to Use the Calculator  
Before using your calculator for the first time, you must reset it and adjust its  
contrast.  
Resetting the calculator  
1. Press the RESET switch located on the  
back of the calculator with the tip of a ball-  
point pen or similar object. Do not use an  
object with a breakable or sharp tip.  
• If you do not see the message on the  
right, the battery may be installed  
incorrectly; refer to ‘Battery Replacement’  
(See page 115.) and try installing it again.  
zALL DATA CL?z  
z YES¬[DEL] z  
z NO¬[ENTER]z  
2. Press y.  
NORMAL MODE  
0.  
• The initial display of the NORMAL mode  
appears.  
3. Press @ o 0 and press + or  
- to adjust the display contrast until it  
is set correctly, then press j.  
LCD CONTRAST  
[+] [-]  
DARK® ¬LIGHT  
• @ o means you have to press @  
followed by S key.  
• See ‘The OPTION menu’ (See page 118.) for more information  
regarding optional functions.  
11  
Chapter 1: Before You Get Started  
The Hard Case  
Your calculator comes with a hard case to protect the keyboard and display  
when the calculator is not in use.  
Before using the calculator, remove the hard case and slide it onto the back  
as shown to avoid losing it.  
When you are not using the calculator, slide the hard case over the keyboard  
and display as shown.  
• Firmly slide the hard case all the way to the edge.  
• The quick reference card is located inside the hard case.  
• Remove the hard case while holding with fingers placed in the positions  
shown below.  
12  
Chapter 1: Before You Get Started  
Calculator Layout and Display Symbols  
Calculator layout  
1 Display screen  
2 Power ON/OFF  
and Clear key  
3 Key operation  
4 Cursor keys  
keys  
1 Display screen: The calculator display consists of 14 × 3 line dot matrix  
display (5 × 7 dots per character) and a 2-digit exponent display per each  
line.  
2 Power ON/OFF and Clear key: Turns calculator ON. To turn off the  
calculator, press @, then o. This key can also be used to clear the  
display.  
3 Key operation keys:  
@: Activates the second function (printed in orange) assigned to the  
next pressed key.  
;: Activates the variable (printed in blue) assigned to the next  
pressed key.  
4 Cursor keys: Enables you to move the cursor in four directions.  
13  
Chapter 1: Before You Get Started  
Display  
Symbol  
Dot matrix  
display  
Exponent  
Mantissa  
• During actual use, not all symbols are displayed at the same time.  
• Only the symbols required for the usage under instruction are shown in the  
display and calculation examples of this manual.  
Indicates some contents are hidden in the directions shown.  
:
Press cursor keys to see the remaining (hidden) section.  
BUSY : Appears during the execution of a calculation.  
2ndF : Appears when @ is pressed.  
xy/rθ : Indicates the mode of expression of results in the complex  
calculation mode.  
HYP : Indicates that H has been pressed and the hyperbolic functions  
are enabled. If @ > are pressed, the symbols ‘2ndF HYP’  
appear, indicating that inverse hyperbolic functions are enabled.  
ALPHA: Appears when ;, @ a, x or t is pressed.  
FIX/SCI/ENG: Indicates the notation used to display a value.  
DEG/RAD/GRAD: Indicates angular units.  
: Appears when statistics mode is selected.  
M
: Indicates that a value is stored in the M memory.  
14  
Chapter 1: Before You Get Started  
Operating Modes  
This calculator has five operating modes to perform various operations.  
These modes are selected from the MODE key.  
Selecting a mode  
1. Press b.  
<MODE-1>  
The menu display appears.  
ƒNORMAL ⁄STAT  
Press d to display the next menu  
¤PROG ‹EQN  
page.  
<MODE-2>  
›CPLX  
2. Press 0 to select the NORMAL mode.  
NORMAL MODE  
• In the menu display, press the assigned  
0.  
number to choose or recall a selection.  
What you can do in each mode  
NORMAL mode:  
Allow you to perform standard scientific calculations, Differential/Integral  
functions, N-base calculations, Solver function, Simulation calculation.  
STAT (statistics) mode:  
Allows you to perform statistical calculations.  
PROG (program) mode:  
Allows you to create and use programs to automate simple or complex  
calculations.  
EQN (equation) mode:  
Allows you to perform equation solvers, such as quadratic equation.  
CPLX (complex) mode:  
Allows you to perform arithmetic operations with complex numbers.  
15  
Chapter 1: Before You Get Started  
A Quick Tour  
This section takes you on a quick tour covering the calculator’s simple  
arithmetic operations and also principal features like the solver function.  
Turning the calculator on and off  
1. Press j at the top right of the keypad  
NORMAL MODE  
to turn the calculator on.  
0.  
• To conserve the batteries, the calculator  
turns itself off automatically if it is not used  
for several minutes.  
2. Press @ o to turn the calculator off.  
• Whenever you need to execute a function or command which is written  
in orange above a key, press @ followed by the key.  
Entering and solving an expression  
Arithmetic expressions should be entered in the same order as they would  
normally be written in. To calculate the result of an expression, press e at  
the bottom right of the keypad; this has the same function as the ‘equals’ key  
on some calculators.  
Example  
Find the answer to the expression  
82 ÷ Ȉȉ3 – 7 × -10.5  
1. 8 A z @ * 3 -  
NORMAL MODE  
0.  
8Œ©‰3-7˚–10.5_  
7 k S 10.5  
• This calculator has a minus key -  
for subtraction and a negative key S  
for entering negative numbers.  
• To correct an error, use the cursor keys  
l r u d to move to the appropriate position on the  
display and type over the original expression.  
2. Press e to obtain an answer.  
0.  
• While the calculator is computing an  
answer, BUSY is displayed at the above  
left of the display.  
8Œ©‰3-7˚–10.5=  
110.4504172  
• The cursor does not have to be at the  
end of an expression for you to obtain  
an answer.  
16  
Chapter 1: Before You Get Started  
Editing an expression  
After obtaining an answer, you can go back to an expression and modify it  
using the cursor keys just as you can before the e is pressed.  
Example  
Return to the last expression and change it to  
82 ÷ Ȉ3 – 7 × -10.5  
1. Press d or r to return to the  
8Œ©‰3-7˚–10.5=  
110.4504172  
8Œ©‰3-7˚–10.5  
last expression.  
• The cursor is now at the beginning of  
the expression (on ‘8’ in this case).  
• Pressing u or l after obtaining  
an answer returns the cursor to the end  
of the last expression.  
• To make the cursor easier to see in diagrams throughout the manual,  
it is depicted as ‘_’ under the character though it may actually appear  
as a rectangular cursor on the display.  
2. Press r four times to move the  
8Œ©‰3-7˚–10.5=  
110.4504172  
8Œ©‰3-7˚–10.5  
cursor to the point where you wish to  
make a change.  
• The cursor has moved four places to the  
right and is now flashing over ‘3’.  
3. Press @ O.  
• This changes the character entering mode from ‘overwrite’ to ‘insert’.  
• When @ is pressed the 2ndF symbol should appear at the above  
of the display. If it does not, you have not pressed the key firmly  
enough.  
• The shape of the flashing cursor tells you which character entering  
mode you are in. A triangular cursor indicates ‘insert’ mode while a  
rectangular cursor indicates ‘overwrite’ mode.  
4. Press ( and then move the cursor  
110.4504172  
8Œ©‰(3-7˚–10.5  
to the end of expression (@ r).  
• Note that the cursor has moved to the  
second line since the expression now  
exceeds 14 characters.  
5. Press ) and e to find the  
answer for the new expression.  
8Œ©‰(3-7˚–10.5  
)=  
7.317272966  
17  
Chapter 1: Before You Get Started  
Using variables  
You can use 27 variables (A-Z and θ) in the NORMAL mode. A number  
stored as a variable can be recalled either by entering the variable name or  
using t.  
Example 1  
Store 23 to variable R.  
1. Press j 2 1 then x.  
NORMAL MODE  
• j clears the display.  
0.  
• ALPHA appears automatically when you  
2„Ò_  
press x. You can now enter any  
alphabetic character or θ (written in blue  
above keys in the keypad).  
2. Press R to store the result of 23 in R.  
0.  
• The stored number is displayed on the  
next line.  
• ALPHA disappears from the display.  
2„ÒR  
8.  
You can also store a number directly  
rather than storing the result of an expression.  
Example 2  
Find the area of a circle which has radius R.  
r
S = πr2  
Enter an expression containing variable R (now equal to 8) from the last  
example.  
1. Press j @ s then ;.  
• Whenever you need to use a character  
NORMAL MODE  
0.  
written in blue on the keypad, press  
; beforehand. ALPHA will appear at  
π_  
the above of the display.  
2. Press R and then A.  
• ALPHA disappears after you have  
NORMAL MODE  
0.  
entered a character.  
πRŒ_  
18  
Chapter 1: Before You Get Started  
3. Press e to obtain the result.  
0.  
πRŒ=  
Follow the same procedure as above,  
but press t instead of ; in  
step 1.  
201.0619298  
You will get the same result.  
Using simulation calculations (ALGB)  
If you want to find more than one solution using the same formula or  
algebraic equation, you can do this quickly and simply by use of the  
simulation calculation.  
Example  
h
Find the volume of two cones:  
1 with height 10 and radius 8 and  
2 with height 8 and radius 9.  
r
1
V = πr2h  
3
1. Press j 1 k 3 @ s  
NORMAL MODE  
1ı3πRŒH_  
; R A ; H to enter the  
0.  
0.  
8.  
formula.  
• Note that ‘1 3’ represents 1 over (i.e.  
divided by) 3.  
• Variables can be represented only by  
capital letters.  
2. Press @ G (I key) to finish  
1ı3πRŒH  
H=z  
entering the equation.  
• The calculator automatically picks out  
the variables alphabetically contained in  
the equation in alphabetical order and  
asks you to input numbers for them.  
•
at the bottom of the display reminds you that there is another  
variable further on in the expression.  
3. Press 10 e to input the height and  
1ı3πRŒH  
R=z  
go on the next variable.  
• The calculator is now asking you to  
input a number for the next variable.  
19  
Chapter 1: Before You Get Started  
• Note that, as the variable R already has a number stored in memory,  
the calculator recalls that number.  
•
indicates that there is another variable earlier in the expression.  
4. Press 8 to input the radius.  
Input of all variables is now complete.  
5. Press e to obtain the solution.  
1ı3πRŒH=  
670.2064328  
•
The answer (volume of cone ᕃ) is  
displayed on the third line.  
6. Press e and 8 to input the height  
1ı3πRŒH  
H=8_  
for cone ᕄ.  
• The display returns to a value entry  
screen with ‘8’ substituted for ‘10’ in  
variable H.  
7. Press e to confirm the change.  
1ı3πRŒH  
R=z  
8.  
8. Press 9 to enter the new radius then  
press e to solve the equation.  
1ı3πRŒH=  
• The volume of cone ᕄ is now displayed.  
• In any step, press @ h to obtain  
the solution using the values entered  
into the variables at that time.  
678.5840132  
20  
Chapter 1: Before You Get Started  
Using the solver function  
You can solve any unknown variable in an equation by assigning known  
values to the rest of the variables. Let us compare the differences between  
the solver function and the simulation calculations using the same expres-  
sion as in the last example.  
Example  
What is the height of cone 3 if it has a radius of 8  
and the same volume as cone 2 (r = 9, h = 8) in  
h
the last example?  
r
1
V = πr2h  
3
9. Store the result of step 8 on the  
0.  
678.5840132  
previous page in variable V.  
Press j twice and ; <  
x V.  
AnsÒV  
10. Input the equation (including ‘=’) in the  
NORMAL mode.  
AnsÒV  
678.5840132  
V=1ı3πRŒH_  
Press ; V ; = then input  
the rest of the expression.  
You must press ; = ( m  
key), not e, to enter the = sign.  
11. Press I 5 to move to the  
V=1ı3πRŒH  
H=z  
variable input display.  
• Note that the values assigned to the  
variables in the last example for the  
simulation calculations are retained and  
displayed.  
8.  
12. Press d to skip the height, and  
then press 8 e to enter the radius  
(R).  
V=1ı3πRŒH  
V=z678.5840132  
• The cursor is now on V. The value that  
was stored in step 9 is displayed.  
(volume of cone 2)  
13. Press u u to go back to the  
V=1ı3πRŒH  
variable H.  
• This time the value of H from memory is  
also displayed.  
H=z  
8.  
21  
Chapter 1: Before You Get Started  
14. Press @ h to find the height of  
H=  
10.125  
cone 3.  
R¬ 678.5840132  
L¬ 678.5840132  
• Note that the calculator finds the  
value of the variable that the cursor is  
on when you press @ h.  
• Now you have the height of cone 3  
that has the same volume as cone  
2.  
Right and left sides of the  
expression after substituting  
the known variables  
Height of cone 3  
• R→ and L→ are the values computed  
by Newton's method, which is used to determine the accuracy of  
the solution.  
Other features  
Your calculator has a range of features that can be used to perform many  
calculations other than those we went through in the quick tour. Some of the  
important features are described below.  
Statistical calculations:  
You can perform one- and two- variable weighted statistical calculations,  
regression calculations, and normal probability calculations. Statistical  
results include mean, sample standard deviation, population standard  
deviation, sum of data, and sum of squares of data. (See Chapter 4.)  
Equation solvers:  
You can perform solvers of simultaneous linear equation with two/three  
unknowns or quadratic/cubic equation. (See Chapter 5.)  
Complex number calculations:  
You can perform addition, subtraction, multiplication, and division  
calculations. (See Chapter 6.)  
Programming:  
You can program your calculator to automate certain calculations. Each  
program can be used in either the NORMAL or NBASE program modes.  
(See Chapter 7.)  
22  
Chapter 2  
General Information  
Clearing the Entry and Memories  
2
*
Multi-entry  
Saved equations  
including saved  
local variables  
4
*
STAT  
Operation  
Entry  
(Display)  
Local  
variables  
recall,  
3
1
5
*
*
*
ANS  
A-Z,  
θ
STAT VAR  
j
×
×
×
×
×
×
×
×
×
×
×
×
×
×
6
*
Mode selection  
×
@ P 0  
@ P 1 y  
@ P 2 y  
@ P 3 y  
RESET switch  
×
×
×
×
: Clear  
: Retain  
×
1
*
*
*
*
*
*
Global variable memories.  
Saved equations and local variables by the filing equations function  
Last answer memory.  
Statistical data (entered data)  
n, x¯, sx, σx, Σx, Σx2, y¯, sy, σy, Σy, Σy2, Σxy, a, b, c, r.  
Will be cleared when changing between sub-modes in the STAT mode.  
2
3
4
5
6
Note:  
• To clear one variable memory of global variable and local variable  
memories, press j x and then choose memory.  
Memory clear key  
Press @ P to display the menu.  
• To initialize the display mode, press 0.  
The parameters set as follows.  
• Angular unit: DEG (See page 26.)  
• Display notation: NORM1 (See page 26.)  
• N-base: DEC (See page 44.)  
<M-CLR>  
ƒDISP ⁄MEMORY  
¤STAT ‹RESET  
• To clear all variables (excluding local variables of saved equations,  
statistical data and STAT variables), press 1 y.  
• To clear statistical data and STAT variables, press 2 y.  
• To RESET the calculator, press 3 y. The RESET operation will  
erase all data stored in memory and restore the calculator’s default setting.  
23  
Chapter 2: General Information  
Editing and Correcting an Equation  
Cursor keys  
Incorrect keystrokes can be changed by using the cursor keys  
(l r u d).  
Example  
Enter 123456 then correct it to 123459.  
1. Press j123456.  
NORMAL MODE  
0.  
123456_  
2. Press y 9 e.  
0.  
• If the cursor is located at the right end  
of an equation, the y key will  
function as a backspace key.  
123459=  
123459.  
• You can return to the equation just after  
getting an answer by pressing the cursor keys. After returning to the  
equation, the following operations are useful;  
@ l or @ r: To jump the cursor to the beginning or the  
end of equation.  
Overwrite mode and insert mode  
• Pressing @ Oswitches between the two editing modes: overwrite  
mode (default); and insert mode. A rectangular cursor indicates preexisting  
data will be overwritten as you make entries, while a triangular cursor  
indicates that an entry will be inserted at the cursor.  
• In the overwrite mode, data under the cursor will be overwritten by the  
number you enter. To insert a number in the insert mode, move the cursor  
to the place immediately after where you wish to insert, then make the  
desired entry.  
• The mode set will be retained until @ Ois pressed or a RESET  
operation is performed.  
24  
Chapter 2: General Information  
Delete key  
• To delete a number/function, move the cursor to the number/function you  
wish to delete, then press y. If the cursor is located at the right end of  
an equation, the y key will function as a backspace key.  
Multi-entry recall function  
Previous equations can be recalled in the NORMAL, STAT or CPLX mode.  
Up to 160 characters of equations can be stored in memory.  
When the memory is full, stored equations are deleted in the order of the  
oldest first.  
• Pressing @ g will display the previous equation. Further pressing  
@ g will display preceding equations.  
• You can edit the equation after recalling it.  
• The multi-entry memory is cleared by the following operations: mode  
change, memory clear (@ P1 y), RESET, N-base conver-  
sion.  
Example  
Input three expressions and then recall them.  
1 3(5+2)=  
2 3×5+2=  
3 3×5+3×2=  
1. Press j3 ( 5 + 2 ) e  
17.  
3 k 5 + 2 e  
3 k 5 + 3 k2 e  
3˚5+3˚2=  
21.  
2. Press @ g to recall the  
3˚5+3˚2=  
3˚5+3˚2  
expression 3.  
21.  
3. Press @ g to recall the  
3˚5+3˚2=  
3˚5+2  
expression 2.  
21.  
21.  
4. Press @ g to recall the  
3˚5+3˚2=  
3(5+2)  
expression 1.  
25  
Chapter 2: General Information  
The SET UP menu  
The SET UP menu enables you to change the angular unit and the display  
format.  
• Press @ Jto display the SET UP  
<SET UP>  
menu.  
ƒDRG ⁄FSE  
• Press jto exit the SET UP menu.  
¤---  
Determination of the angular unit  
The following three angular units (degrees,  
radians, and grads) can be specified.  
• DEG(°) : Press @ J0 0  
• RAD (rad): Press @ J0 1  
• GRAD (g): Press @ J0 2  
Selecting the display notation and number of decimal places  
Five display notation systems are used to display calculation results: Two  
settings of Floating point (NORM1 and NORM2), Fixed decimal point (FIX),  
Scientific notation (SCI) and Engineering notation (ENG).  
• When @ J1 0 (FIX) or @ J1 2 (ENG) is  
pressed, ‘TAB(0-9)?’ will be displayed and the number of decimal places  
(TAB) can be set to any value between 0 and 9.  
• When @ J1 1 (SCI) is pressed, ‘SIG(0-9)?’ will be dis-  
played and the number of significant digits (SIG) can be set to any value  
between 0 and 9. Entering 0 will set a 10-digit display.  
• When a floating point number does not fit in the specified range, the  
calculator will display the result using the scientific notation (exponential  
notation) system. See the next section for details.  
Setting the floating point numbers system in scientific  
notation  
The calculator has two settings for displaying a floating point number:  
NORM1 (default setting) and NORM2. In each display setting, a number is  
automatically displayed in scientific notation outside a preset range:  
• NORM1: 0.000000001 ≤ |x| ≤ 9999999999  
• NORM2: 0.01 ≤ |x| ≤ 9999999999  
26  
Chapter 2: General Information  
Example  
Key operations  
Result  
100000÷3=  
[Floating point (NORM1)]  
j@ J1 3  
100000z3e  
@ J1 0 2  
33333.33333  
33333.33  
→[FIXed decimal point  
and TAB set to 2]  
→[SCIentific notation  
and SIG set to 3]  
→[ENGineering notation  
and TAB set to 2]  
→[Floating point (NORM1)]  
3.33˚1004  
33.33˚1003  
@ J1 1 3  
@ J1 2 2  
@ J1 3  
33333.33333  
3÷1000=  
[Floating point (NORM1)]  
j3z1000e  
0.003  
3.˚10-03  
0.003  
→[Floating point (NORM2)] @ J1 4  
→[Floating point (NORM1)]  
@ J1 3  
Using Memories  
The calculator uses global variable memories (A–Z and θ), local variable  
memories (maximum of nine variables per equation), and a last answer  
memory used when solving equations.  
Using alphabetic characters  
You can enter an alphabetic character (written  
in blue) when ALPHA is displayed at the top of  
NORMAL MODE  
0.  
the display. To enter this mode, press ;.  
To enter more than one alphabetic character,  
press @ a to apply the alphabet-lock  
mode. Press ; to escape from this mode.  
Using global variables  
You can assign values (numbers) to global variables by pressing xthen  
A–Z and θ.  
Example 1  
Store 6 in global variable A.  
1. Press j6 xA.  
• There is no need to press ; because  
ALPHA is selected automatically when  
you press x.  
0.  
6ÒA  
6.  
27  
Chapter 2: General Information  
Example 2  
Recall global variable A.  
1. Press tA.  
6.  
6.  
• There is no need to press ; because  
ALPHA is selected automatically when  
you press t.  
A=  
Using local variables  
Nine local variables can be used in each equation or program, in addition to  
the global variables. Unlike global variables, the values of the local variables  
will be stored with the equation when you save it using the filing equations  
function. (See page 58.)  
To use local variables, you first have to assign the name of the local variable  
using two characters: the first character must be a letter from A to Z or θ and  
the second must be a number from 0 to 9.  
Example  
Store 1.25 x 10-5 as local variable A1 (in the NORMAL mode) and  
recall the stored number.  
1. Press @ v.  
ƒz ‹ fl  
• The VAR menu appears.  
• If no local variables are stored yet,  
ALPHA appears automatically and the  
⁄ › ‡  
¤ fi °  
calculator is ready to enter a name.  
2. Press A1 e.  
¬ƒA¡ ‹ fl  
⁄ › ‡  
¤ fi °  
•
shows that you have finished assigning  
the name A1.  
¬
• To assign more names, press d to  
move the cursor to VAR 1 and repeat the  
process above.  
3. Press j.  
• This returns you to the previous screen.  
4. Press 1.25 ` S5 x@  
0.  
v 0.  
1.25E–5ÒA1  
0.0000125  
28  
Chapter 2: General Information  
• You do not need to enter an alphabetic character. Just specify the  
named local variable using a number from 0 to 8, or move the arrow  
to the appropriate variable the press e.  
5. Press @ v 0 e.  
0.0000125  
• The value of VAR 0 will be recalled.  
• Alternatively you can recall a variable by  
moving the arrow to it then press e  
A1=  
0.0000125  
twice.  
Note:  
• You can change the name of a local variable by overwriting it in the VAR  
menu. The cursor appears when r is pressed in the VAR menu.  
• Local variables not stored using the filing equations function will be  
deleted by mode selection or memory clear operation (@ P  
1 y).  
• Local and global variables will be cleared by creating a new program,  
and editing and running a program.  
Using variables in an equation or a program  
Both global and local variables can be used directly in an equation or a  
program. Local variables are useful when you need to use variables such as  
X1 and X2 at the same time in another equation. The local variable names  
and their values can be saved in each equation. (See page 58.)  
Example  
Using A (6) and A1 (0.0000125) from the last two examples, solve the  
expression.  
1
A1  
—
– 1000A  
1. Press j1 k.  
• Start entering the expression.  
NORMAL MODE  
1ı_  
0.  
2. Press @ v.  
¬ƒA¡ ‹ fl  
⁄ › ‡  
¤ fi °  
3. Press 0 - 1000 ; A e.  
• The display returns automatically to the  
previous screen after you have chosen  
the local variable, and you can continue  
to enter the expression.  
• You do not need kif you use a  
variable. However, the variable must be  
a multiplier.  
0.  
1ıA¡-1000A=  
74000.  
29  
Chapter 2: General Information  
Using the last answer memory  
The calculator always keeps the most recent answer in ANS memory and  
replaces it with the new answer every time you press an ending instruction  
(e, xetc.). You may recall the last answer and use it in the next  
equation.  
Example  
Evaluate the base area (S = 32π) and  
volume of a cylinder (V = 5S) using the last  
answer memory.  
h = 5  
r = 3  
1. Press j3 A@ se.  
• The area of the base is now calculated.  
• The number 28.27433388 is held in ANS  
memory.  
0.  
3Œπ=  
28.27433388  
2. Press j5 ; < e.  
• You now have the volume of the  
cylinder.  
0.  
5Ans=  
141.3716694  
The last answer is cleared (i.e. set to 0) if you  
press the RESET switch, change the mode or memory clear operation (@  
P1 y), but not if you turn the calculator off.  
Global variable M  
Using the M memory, in addition to the features of global variables, a value  
can be added to or subtracted from an existing memory value.  
Example  
Key operations  
Result  
jxM  
0.  
$150×3:Ma  
150 k3m  
450.  
250.  
35.  
+)$250:Mb=Ma+250  
250 m  
tMk5@ %  
@ MtM  
–)Mb×5%  
M
665.  
• m and @ Mcannot be used in the STAT mode.  
30  
Chapter 2: General Information  
Using memory in each mode  
Mode  
ANS  
M
A-L, N-Z,  
Local variables  
NORMAL  
STAT  
PROG  
EQN  
CPLX  
: Available  
: Unavailable  
Notes:  
• Calculation results from the functions indicated below are automati-  
cally stored in memories replacing any existing values.  
• →rθ, →xy.................. R memory (r)  
θ memory (θ)  
X memory (x)  
Y memory (y)  
• Use of tor ; will recall the value stored in memory using up  
to 14 digits in accuracy.  
31  
Chapter 2: General Information  
Resetting the calculator  
If you wish to clear all memories, variables, files and data, or if none of the  
keys (including j) will function, press the RESET switch located on the  
back of the calculator.  
In rare cases, all the keys may cease to function if the calculator is subjected  
to strong electrical noise or heavy shock during use. Follow the instructions  
below to reset the calculator.  
Caution:  
• The RESET operation will erase all data stored in memory and  
restore the calculator's default setting.  
1. Press the RESET switch located on the  
back of the calculator with the tip of a ball-  
point pen or similar object. Do not use an  
object with a breakable or sharp tip.  
• A display appears asking you to confirm  
that you really want to reset the calculator.  
zALL DATA CL?z  
z YES¬[DEL] z  
z NO¬[ENTER]z  
2. Press y.  
z ALL DATA z  
z CLEARED! z  
• All memories, variables, files and data are  
cleared.  
z
z
• The display goes back to the initial display in  
the NORMAL mode.  
NORMAL MODE  
• The calculator will revert to the very first  
settings that were made when you started  
to use the calculator for the first time.  
0.  
Or, to cancel the operation, press e.  
Note:  
• When corruption of data occurs, the reset procedure may automati-  
cally be initiated upon pressing the RESET switch.  
• Pressing @ Pand 3 y can also clear all memories,  
variables, files and data as described above.  
32  
Chapter 3  
Scientific Calculations  
NORMAL mode  
NORMAL mode is used for standard scientific calculations, and has the  
widest variety of functions. Many of the functions described in this chapter  
are also available for use in other modes.  
Press b0 to select the NORMAL mode.  
• Differential/Integral functions, N-base functions, Solver functions and  
Simulation Calculation (ALGB) in this chapter are all performed in the  
NORMAL mode.  
• In each example of this chapter, press j to clear the display first. If  
the FIX, SCI or ENG indicator is displayed, clear the indicator by  
selecting ‘NORM1’ from the SET UP menu. Unless specified, set the  
angular unit as ‘DEG’. (@ P 0)  
Arithmetic operations  
Example  
45+285÷3=  
Key operations  
Result  
140.  
j45+ 285z3  
e
18+6  
15–8  
( 18+ 6) z  
=
( 15- 8) e  
3.428571429  
–90.  
42×(–5)+120=  
42kS5+ 120e  
(5×103)÷(4×10–3)= 5` 3z4` S  
3e  
1250000.  
33  
Chapter 3: Scientific Calculations  
Constant calculations  
Example  
34+57=  
Key operations  
34+ 57e  
45  
Result  
91.  
102.  
45+57=  
68×25=  
68×40=  
e
1700.  
2720.  
68k25e  
40e  
• In constant calculations, the addend becomes a constant. Subtraction  
and division behave the same way. For multiplication, the multiplicand  
becomes a constant.  
• In constant calculations, constants will be displayed as ∆.  
Functions  
Example  
sin60 [°]=  
Key operations  
jv60e  
0 1 $  
@ sk  
Result  
0.866025403  
π
@
J
cos — [rad]=  
4
4
e
0.707106781  
50.  
tan–11 [g]=  
@
e
J
0 2 @ y  
1
@ P0  
• The range of the results of inverse trigonometric functions  
θ = sin–1 x  
,
θ= tan–1 x  
θ= cos x  
–1  
DEG  
–90 ≤  
θ
≤ 90  
0 ≤  
θ
≤ 180  
π
π
—
—
RAD  
–
0
π
≤
≤
θ
θ
≤
≤
θ
≤
2
2
GRAD  
–100  
100  
0
200  
≤
≤
θ
≤
34  
Chapter 3: Scientific Calculations  
Example  
Key operations  
Result  
(cosh 1.5 +  
sinh 1.5)2 =  
j( H$ 1.5+  
Hv1.5) Ae  
20.08553692  
@ > t (  
5
5
tanh–1— =  
7
z
i
l
7
) e  
0.895879734  
2.995732274  
1.698970004  
20.08553692  
50.11872336  
ln 20 =  
log 50 =  
e3 =  
20  
50  
e
e
@ "  
3e  
101.7  
=
@ Y1.7e  
1
6 @ Z+  
Ze  
7
@
1
— + — =  
6
7
0.309523809  
-2024.984375  
8–2 – 34 × 52 =  
8
4
mS  
2
-
3
m
k
5
Ae  
1
12  
m
3
m
4
—
3
4
(12 ) =  
@ Ze  
6.447419591  
512.  
83 =  
8
1e  
@ * 49  
81  
@ q 27  
49 –4 81  
=
-
e
4
@ D  
e
4.  
3.  
3
27 =  
4! =  
4
@ Be  
24.  
10P3 =  
10@ e  
3
e
720.  
10.  
5C2 =  
5
@ c  
2e  
500×25%=  
500  
120  
500  
400  
k
z
+
-
25@ %  
400@ %  
25@ %  
30@ %  
125.  
30.  
120÷400=?%  
500+(500×25%)=  
400–(400×30%)=  
625.  
280.  
35  
Chapter 3: Scientific Calculations  
Math menu Functions  
Other functions are available on this calculator besides the first and second  
functions on the key pad. These functions are accessed using the math  
function menu. The math menu has different contents for each mode.  
Press Ito display the math menu. In the NORMAL mode, you can recall  
the following functions.  
<MATH MENU-1>  
ƒabs ⁄ipart  
¤int ‹fpart  
<MATH MENU-2>  
›ÒRAND fiSOLVE  
flΩsec ‡Ωmin  
→
d
• Switch the display using d u.  
• These math menus are not available for Differential/Integral functions,  
N-base functions, Solver functions and Simulation Calculation (ALGB).  
Function  
Key operations  
Result  
abs–7=  
0: abs  
Displays the absolute value of a  
number.  
I0 S  
7
e
7.  
–7.  
–8.  
1: ipart  
Displays the integer part only of a  
number.  
I1 S  
7.94  
ipart–7.94=  
int–7.94=  
e
2: int  
Displays the largest integer less  
than or equal to a number.  
I2 S  
7.94  
e
3: fpart  
Displays the fractional part only of  
a number.  
I3 S  
7.94  
fpart–7.94=  
–0.94  
e
4: ⇒RAND  
Before using the Random Numbers  
of Random functions, designate  
0.001 from 0.999 random number  
sequences available.  
0.001I4  
0.001ÒRAND  
0.001  
0.232  
The calculator can regenerate the  
same random numbers from the  
beginning.  
If you wish to go back to normal  
random numbers, press  
0 I4.  
@ w 0  
e
random=  
36  
Chapter 3: Scientific Calculations  
Function  
Key operations  
Result  
5: SOLVE  
Enter the Solver function mode.  
(See page 52.)  
I 5  
6: Ωsec  
Sexagesimal numbers are  
converted to seconds notation.  
(See page 46.)  
24[ I  
24∂Ωsec  
6
86400.  
7: Ωmin  
Sexagesimal numbers are  
converted to minutes notation.  
(See page 46.)  
0[ 0[  
1500I7  
0∂0∂1500Ωmin  
25.  
37  
Chapter 3: Scientific Calculations  
Differential/Integral Functions  
Differential and integral calculations can only be performed in the NORMAL  
mode. It is possible to reuse the same equation over and over again and to  
recalculate by only changing the values without having to re-enter the  
equation.  
• Performing a calculation will clear the value in the X memory.  
• You can use both global and local variables in the equation.  
• The answer calculated will be stored in the last answer memory.  
• The answer calculated may include a margin of error, or an error may  
occur. In such a case, recalculate after changing the minute interval (dx)  
or subinterval (n).  
• Since differential and integral calculations are performed based on the  
following equations, in certain rare cases correct results may not be  
obtained, such as when performing special calculations that contain  
discontinuous points.  
Integral calculation (Simpson’s rule):  
b – a  
N
N=2n  
a≤x≤b  
1
3
——  
h=  
S=—h{f (a)+4{f (a+h)+f (a+3h)+······+f(a+(N–1)h)}  
+2{f (a+2h)+f (a+4h)+······+f (a+(N–2)h)}+f(b)}  
Differential calculation:  
dx  
2
dx  
2
f(x+––)–f(x–––)  
f’(x)=————————  
dx  
Differential function  
The differential function is used as follows.  
1. Press b0 to enter the NORMAL mode.  
2. Input a formula with an x variable.  
3. Press @ 3.  
4. Input the x value and press e.  
5. Input the minute interval (dx).  
6. Press e to calculate.  
38  
Chapter 3: Scientific Calculations  
• To exit the differential function, press j.  
• After getting the answer, press e to return to the display for inputting  
the x value and the minute interval, and press @ h to recalculate  
at any point.  
Example  
Key operations  
Result  
d/dx (x4–0.5x3+6x2) j; X* m4- 0.5  
; X 1+ 6;  
≈^4-0.5≈„+6≈Œ  
≈=  
0.  
z
dx:  
0.00001  
X A@ 3  
x = 2  
dx = 0.00002  
d/dx = ?  
2e e  
≈^4-0.5≈„+6≈Œ  
d/dx=  
50.  
x = 3  
dx = 0.001  
d/dx = ?  
e 3e 0.001e  
≈^4-0.5≈„+6≈Œ  
d/dx=  
130.5000029  
* X memory is specified by pressing ; then the 3 key.  
Integral function  
The Integral function is used as follows.  
1. Press b0 to enter the NORMAL mode.  
2. Input a formula with an x variable.  
3. Press {.  
4. Input the starting value (a) of a range of integral and press e.  
5. Input the finishing value (b) of a range of integral and press e.  
6. Input the subinterval (n).  
7. Press e to calculate.  
• To exit the integral function, press j.  
• After getting the answer, press e to return to the display for inputting  
a range of integral and subinterval, and press @ h to recalculate  
at any point.  
39  
Chapter 3: Scientific Calculations  
Example  
82 (x2–5)dx  
Key operations  
Result  
j; X A- 5  
∫
a=  
0.  
0.  
z
{
b=  
n=  
100.  
138.  
138.  
n = 100  
dx = ?  
2e 8e e  
≈Œ-5  
∫dx=  
∫
n = 10  
dx = ?  
e e e 10e  
≈Œ-5  
∫dx=  
∫
When performing integral calculations  
Integral calculations require a long calculation time, depending on the  
integrands and subintervals input. During calculation, ‘calculating!’ will be  
displayed. To cancel calculation, press j. Note that there will be greater  
integral errors when there are large fluctuations in the integral values during  
minute shifting of the integral range and for periodic functions, etc., where  
positive and negative integral values exist depending on the interval.  
For the former case, make the integral interval as small as possible. For the  
latter case, separate the positive and negative values.  
Following these tips will provide calculations results with greater accuracy  
and will also shorten the calculation time.  
y
y
x0  
x2  
b
a
x
x
a
b
x0  
x1  
x2  
x3  
x1  
x3  
40  
Chapter 3: Scientific Calculations  
Random Function  
The Random function has four settings for the NORMAL, STAT or PROG  
mode. (This function is not available while using the N-base function, solver  
function and simulation calculations.)  
Random numbers  
A pseudo-random number, with three significant digits from 0 up to 0.999,  
can be generated by pressing @ w 0 e. To generate further  
random numbers in succession, press e. Press j to exit.  
• The calculator can regenerate the same random number. (See page 36.)  
Random dice  
To simulate a die-rolling, a random integer between 1 and 6 can be gener-  
ated by pressing @ w 1 e. To generate further random  
numbers in succession, press e. Press j to exit.  
Random coin  
To simulate a coin flip, 0 (head) or 1 (tail) can be randomly generated by  
pressing @ w 2 e. To generate further random numbers in  
succession, press e. Press j to exit.  
Random integer  
An integer between 0 and 99 can be generated randomly by pressing @  
w 3 e. To generate further random numbers in succession, press  
e. Press j to exit.  
Example  
Key operations  
Result  
Pick a random  
number between  
0 and 9.99.  
j @ w 0  
0.  
k 10e  
random˚10=  
6.31  
• The result may not be the same each time this operation is performed.  
41  
Chapter 3: Scientific Calculations  
Angular Unit Conversions  
The angular unit is changed in sequence each time @ ] ( . key)  
is pressed.  
Example  
90°→ [rad]  
Key operations  
Result  
j90@ ]  
@ ]  
1.570796327  
100.  
→ [g]  
→ [°]  
@ ]  
90.  
sin–10.8 = [°]  
→ [rad]  
→ [g]  
@ w0.8e  
@ ]  
53.13010235  
0.927295218  
59.03344706  
53.13010235  
@ ]  
→ [°]  
@ ]  
Chain Calculations  
The previous calculation result can be used in a subsequent calculation.  
However, it cannot be recalled after entering multiple instructions.  
• When using postfix functions (  
, sin, etc.), a chain calculation is  
possible even if the previous calculation result is cleared by the use of  
the j key.  
Example  
6+4=ANS  
Key operations  
Result  
j
6+ 4e  
10.  
15.  
ANS+5  
+ 5e  
8×2=ANS  
8k2e  
16.  
ANS2  
A
e
256.  
44+37=ANS  
ANS=  
44+ 37e  
81.  
9.  
@ * e  
42  
Chapter 3: Scientific Calculations  
Fraction Calculations  
Arithmetic operations and memory calculations can be performed using  
fractions, and conversions between decimal numbers and fractions.  
• If the number of digits to be displayed is greater than 10, the number is  
converted to and displayed as a decimal number.  
Example  
Key operations  
Result  
1
2
4
3
b
3— + — = [a—]  
j3k 1k 2+  
4k 3e  
k
c
4ı5ı6  
*
→[a.xxx]  
4.833333333  
29ı6  
→[d/c]  
@ F  
2
—
3
=
@ Y2k 3e  
4.641588834  
16807ı3125  
10  
5
7
5
— =  
7k 5m5e  
( )  
1
3
—
1
1 k 8 m1k 3e  
—
=
1ı2  
( )  
8
64  
—— =  
@ * 64k 225e  
8ı15  
225  
23  
( 2m3) k  
( 3m4) e  
— =  
34  
8ı81  
1.2  
—– =  
2.3  
1.2k 2.3e  
12ı23  
1°2’3”  
2
——– =  
1[  
2
[ 3k 2e  
0∂31∂1.5∂  
1ı2  
1×103  
——– =  
1` 3k 2` 3e  
2×103  
A = 7  
j7xA  
7.  
4
A
— =  
4k ; Ae  
4ı7  
2
5
1.25 + — = [a.xxx] 1.25+ 2k 5e  
1.65  
b
→[a—]  
k
1ı13ı20  
c
5
6
*
4ı5ı6= 4—  
43  
Chapter 3: Scientific Calculations  
Binary, Pental, Octal, Decimal, and Hexadecimal  
Operations (N-base)  
This calculator can perform conversions between numbers expressed in  
binary, pental, octal, decimal and hexadecimal systems. It can also perform  
the four basic arithmetic operations, calculations with parentheses and  
memory calculations using binary, pental, octal, decimal, and hexadecimal  
numbers. Furthermore, the calculator can carry out the logical operations  
AND, OR, NOT, NEG, XOR and XNOR on binary, pental, octal and hexadeci-  
mal numbers.  
Conversion to each system is performed by the following keys:  
@ z: Converts to the binary system. ‘?’ appears.  
@ r: Converts to the pental system. ‘q’ appears.  
@ g: Converts to the octal system. ‘f’ appears.  
@ h: Converts to the hexadecimal system. ‘6’ appears.  
@ /: Converts to the decimal system. ‘?’, ‘q’, ‘f’ and ‘6’ disappear  
from the display.  
Conversion is performed on the displayed value when these keys are  
pressed.  
Note: Hexadecimal numbers A – F are entered into the calculator by  
pressing ,, m, A, 1, l, and ikey respectively.  
In the binary, pental, octal, and hexadecimal systems, fractional parts cannot  
be entered. When a decimal number having a fractional part is converted  
into a binary, pental, octal, or hexadecimal number, the fractional part will be  
truncated. Likewise, when the result of a binary, pental, octal, or hexadecimal  
calculation includes a fractional part, the fractional part will be truncated. In  
the binary, pental, octal, and hexadecimal systems, negative numbers are  
displayed as a complement.  
44  
Chapter 3: Scientific Calculations  
Example  
Key operations  
Result  
DEC(25)→BIN  
j@ / 25@ z  
11001 b  
.
HEX(1AC)  
→BIN  
→PEN  
→OCT  
→DEC  
@ a1AC  
@ z  
@ r  
@ g  
@ /  
110101100 b  
3203 P  
654 0  
428.  
.
.
.
BIN(1010–100)  
×11 =  
@ z ( 1010- 100  
) k11e  
10010 b  
1111111001 b  
.
BIN(111)→NEG  
d111e  
.
HEX(1FF)+  
OCT(512)=  
HEX(?)  
@ a1FF@ g+  
512e  
@ a  
1511 0  
349 H  
.
.
2FEC–  
2C9E=(A)  
+)2000–  
1901=(B)  
(C)  
jxM@ a 2FEC  
- 2C9Em  
2000-  
1901m  
tM  
34E H  
.
6FF H  
A4D H  
.
.
1011 AND  
101 = (BIN)  
j@ z 10114  
101e  
1b  
DB H  
1111101001 b  
.
5A OR C3 = (HEX) @ a5ApC3e  
.
NOT 10110 =  
(BIN)  
@ z n 10110e  
.
24 XOR 4 = (OCT) @ g24x 4e  
20 0  
.
B3 XNOR  
2D = (HEX)  
→DEC  
@ aB3C  
2De  
@ /  
FFFFFFFF61 H  
–159.  
.
45  
Chapter 3: Scientific Calculations  
Time, Decimal and Sexagesimal Calculations  
Conversion between decimal and sexagesimal numbers can be performed,  
and, while using sexagesimal numbers, also conversion to seconds and  
minutes notation. The four basic arithmetic operations and memory calcula-  
tions can be performed using the sexagesimal system. Notation for  
sexagesimal is as follows:  
12∂34∂56.78∂  
degree  
second  
minute  
Example  
Key operations  
Result  
12°39’18.05”  
→[10]  
j12[ 39[ 18.05  
@ :  
12.65501389  
123.678→[60]  
123.678@ :  
123∂40∂40.8∂  
3h30m45s +  
3[ 30[ 45+ 6 [  
6h45m36s = [60] 45[ 36e  
10∂16∂21.∂  
1234°56’12” +  
1234[ 56[ 12+  
0°0’34.567” = [60] 0[ 0[ 34.567e  
1234∂56∂47.∂  
3h45m –  
3[ 45- 1.69e  
1.69h = [60]  
@ :  
2∂3∂36.∂  
0.884635235  
86400.  
sin62°12’24” = [10] v62[ 12[ 24 e  
24°→[ ” ]  
24[ I6  
1500”→[ ’ ]  
0[ 0[ 1500I7  
25.  
46  
Chapter 3: Scientific Calculations  
Coordinate Conversions  
Conversions can be performed between rectangular and polar coordinates.  
Y
Y
P (x, y)  
P (r,  
θ)  
r
y
θ
X
X
0
0
x
Rectangular coordinate  
Polar coordinate  
• Before performing a calculation, select the angular unit.  
• The calculation result is automatically stored in memories.  
• Value of r: R memory  
• Value of θ: θ memory  
• Value of x: X memory  
• Value of y: Y memory  
• r and x values are stored in the last answer memory.  
Example  
x = 6 r =  
Key operations  
Result  
j6, 4  
@ u  
r
= 7.211102551  
→
θ
y = 4  
= [°]  
= 33.69006753  
r = 14  
x =  
y =  
14, 36  
@ E  
x
= 11.32623792  
→
θ
= 36[°]  
y= 8.228993532  
47  
Chapter 3: Scientific Calculations  
Calculations Using Physical Constants  
Recall a constant by pressing @ c followed by the number of the  
physical constant designated by a 2-digit number.  
The recalled constant appears in the display mode selected with the  
designated number of decimal places.  
Physical constants can be recalled in the NORMAL mode (when not set to  
binary, pental, octal, or hexadecimal), STAT mode, PROG mode and EQN  
mode.  
Note: Physical constants are based either on the 2002 CODATA recom-  
mended values, or the 1995 Edition of the ‘Guide for the Use of the  
International System of Units (SI)’ released by NIST (National Institute  
of Standards and Technology), or on ISO specifications.  
No.  
Constant  
Symbol  
c, c 0  
G
Unit  
m s–1  
m3 kg–1 s–2  
m s–2  
kg  
01 Speed of light in vacuum  
02 Newtonian constant of gravitation  
03 Standard acceleration of gravity  
04 Electron mass  
gn  
me  
mp  
05 Proton mass  
kg  
mn  
06 Neutron mass  
kg  
m
µ
07 Muon mass  
kg  
lu  
e
08 Atomic mass unit-kilogram relationship  
09 Elementary charge  
10 Planck constant  
kg  
C
h
J s  
J K–1  
N A–2  
F m–1  
m
k
11 Boltzmann constant  
12 Magnetic constant  
µ0  
ε0  
re  
α
a0  
R
13 Electric constant  
14 Classical electron radius  
15 Fine-structure constant  
16 Bohr radius  
m
m–1  
17 Rydberg constant  
∞
18 Magnetic flux quantum  
19 Bohr magneton  
Φ0  
µB  
µe  
µN  
µp  
µn  
Wb  
J T–1  
J T–1  
J T–1  
J T–1  
J T–1  
20 Electron magnetic moment  
21 Nuclear magneton  
22 Proton magnetic moment  
23 Neutron magnetic moment  
48  
Chapter 3: Scientific Calculations  
No.  
Constant  
Symbol  
Unit  
24 Muon magnetic moment  
25 Compton wavelength  
µµ  
λc  
J T–1  
m
26 Proton Compton wavelength  
27 Stefan-Boltzmann constant  
28 Avogadro constant  
λc, p  
σ
m
W m–2 K–4  
mol–1  
NΑ  
,
L
29 Molar volume of ideal gas (273.15 K,  
101.325 kPa)  
Vm  
m3 mol–1  
30 Molar gas constant  
R
J mol–1 K–1  
C mol–1  
Ohm  
C kg–1  
m2 s–1  
F
RK  
31 Faraday constant  
32 Von Klitzing constant  
33 Electron charge to mass quotient  
34 Quantum of circulation  
35 Proton gyromagnetic ratio  
36 Josephson constant  
37 Electron volt  
-
e/me  
h/2me  
γp  
s–1 T–1  
Hz V–1  
KJ  
eV  
J
t
K
38 Celsius Temperature  
39 Astronomical unit  
AU  
m
pc  
M(12C)  
m
40 Parsec  
kg mol–1  
41 Molar mass of carbon-12  
42 Planck constant over 2 pi  
43 Hartree energy  
-
h
J s  
J
Eh  
G0  
44 Conductance quantum  
45 Inverse fine-structure constant  
46 Proton-electron mass ratio  
47 Molar mass constant  
48 Neutron Compton wavelength  
49 First radiation constant  
50 Second radiation constant  
51 Characteristic impedance of vacuum  
52 Standard atmosphere  
s
–1  
α
mp/me  
Mu  
kg mol–1  
λc, n  
c1  
m
W m2  
c2  
m K  
Ω
Pa  
Z0  
Example  
Key operations  
Result  
V = 15.3 m/s  
j15.3 k10+ 2@  
Zk@ c 03k10  
Ae  
0
t = 10 s  
1
643.3325  
V t +  
0
gt2 = ? m  
2
49  
Chapter 3: Scientific Calculations  
Calculations Using Engineering Prefixes  
Calculation can be executed in the NORMAL mode (excluding N-base),  
STAT mode and PROG mode using the following 12 types of prefixes.  
Prefix  
Operation  
@ j 0  
Unit  
E
P
T
G
M
k
(Exa)  
1018  
1015  
1012  
109  
106  
103  
10–3  
10–6  
10–9  
10–12  
10–15  
10–18  
(Peta)  
(Tera)  
(Giga)  
(Mega)  
(kilo)  
@ j 1  
@ j 2  
@ j 3  
@ j 4  
@ j 5  
@ j 6  
@ j 7  
@ j 8  
@ j 9  
@ j A  
@ j B  
m
µ
n
(milli)  
(micro)  
(nano)  
(pico)  
(femto)  
(atto)  
p
f
a
Example  
Key operations  
Result  
100m × 10k =  
100 @ j 6 k  
10 @ j 5 e  
1000.  
50  
Chapter 3: Scientific Calculations  
Modify Function  
Calculation results are internally obtained in scientific notation with up to 14  
digits for the mantissa. However, since calculation results are displayed in  
the form designated by the display notation and the number of decimal  
places indicated, the internal calculation result may differ from that shown in  
the display. By using the modify function, the internal value is converted to  
match that of the display, so that the displayed value can be used without  
change in subsequent operations.  
Example  
5÷9=ANS  
ANS×9=  
Key operations  
Result  
j@ J1 0 1  
5z9e  
0.6  
[FIX,TAB=1]  
k9e*1  
5.0  
5z9e @ n  
0.6  
5.4  
k9e*2  
@ P0  
1
*
*
5.5555555555555×10–1×9  
0.6×9  
2
51  
Chapter 3: Scientific Calculations  
Solver Function  
This function enables you to find any variable in an equation.  
Entering and solving an equation  
The solver function is used as follows.  
1. Press b0 to enter the NORMAL mode.  
2. Enter both sides of an equation, using ‘=’ and variable names.  
3. Press I5.  
4. Enter the value of the known variables.  
5. Move the cursor (display) to the unknown variables.  
6. Press @ h.  
• The solver function can find any variable  
NORMAL MODE  
anywhere in an equation. It can even find  
0.  
variables that appear several times in an  
equation.  
TŒ=(4π©GM)R_  
Equation entering display  
• You can use both global and local  
variables in your equation. (See page 58.)  
• Using the solver function will cause variables memory to be overwritten  
with new values.  
• To exit the solver function, press j.  
Changing the value of variables and editing an equation  
When you are in the solution display, press e to return to the display for  
entering values of variables, then return to the equation display in the  
NORMAL mode by pressing j.  
R= 1.127251652  
TŒ=(4π©GM)R  
NORMAL MODE  
0.  
TŒ=(4π©GM)R_  
R¬  
L¬  
9.  
9.  
→
e
→
j
G=z  
1.5  
Solution display  
Use d u to  
move between  
variables.  
52  
Chapter 3: Scientific Calculations  
Solving an equation  
Example  
Try finding the variables in the equation below.  
=
×
×
C
D
A
B
1. Press b0 to select the NORMAL mode.  
2. Press ; A k; B ;  
NORMAL MODE  
= ; C k; D.  
0.  
0.  
• You must enter the whole equation.  
A˚B=C˚D_  
3. Press I5.  
• The calculator automatically calls the  
display for entering variables and  
displays the variables in alphabetical  
order.  
A˚B=C˚D  
A=z  
•
indicates that there are more  
variables.  
• If a variable already has a value, the calculator displays that value  
automatically.  
4. Press 10 e.  
A˚B=C˚D  
B=z  
• Enters a value for known variable A.  
• The cursor moves onto the next  
variable.  
0.  
0.  
5. Press 5 e.  
• Enters a value for known variable B.  
A˚B=C˚D  
C=z  
6. Press 2.5 e.  
A˚B=C˚D  
D=z  
• Enters a value for known variable C.  
• The cursor moves onto the next  
variable. indicates that this is the last  
variable.  
0.  
7. Press @ h.  
D=  
R¬  
L¬  
20.  
50.  
50.  
• After showing the ‘calculating!’ display,  
the calculator finds the value for the  
unknown variable that was indicated  
by the cursor.  
Values of the left-hand side  
of the equation  
Values of the right-hand side  
of the equation  
53  
Chapter 3: Scientific Calculations  
• The value shown on the display for the unknown variable does not  
have to be set to 0 to solve the equation.  
• The answer is displayed on the top line and the values of the left-  
hand and right-hand sides of the equation appear below.  
8. Press e.  
A˚B=C˚D  
• Returns you to the display for entering  
variables.  
A=z  
10.  
2.5  
9. Press d 8 e.  
• Substitutes the value 8 for B.  
• The cursor moves onto the next variable  
C.  
A˚B=C˚D  
C=z  
10. Press @ h.  
• You can find any unknowns in the same  
equation.  
C=  
R¬  
L¬  
4.  
80.  
80.  
Important notes  
There are several important points to remember when you use the solver  
function.  
• To cancel calculation, press j when ‘calculating!’ is displayed.  
• Before entering the equation, the appropriate angular unit must be  
selected.  
• The calculator uses Newton’s method to solve equations. Due to this,  
there may be some equations that it fails to solve even though they are  
in fact solvable. (See page 123.)  
• The calculator stops calculating when the values it has obtained for the  
left and right sides of the equation become very close. Thus in certain  
cases the solution it gives may not be the real answer. (See page 122.)  
• In certain cases, the calculator may abort a calculation and display the  
message shown on the right. (See page  
- ERROR 02 -  
CALCULATION  
121.)  
54  
Chapter 3: Scientific Calculations  
Simulation Calculation (ALGB)  
This function enables you to find different solutions quickly using different  
sets of values in the same expression.  
Entering an expression for simulation calculation  
The simulation calculation is used as follows.  
1. Press b0 to enter the NORMAL mode.  
2. Enter an expression with at least one variable.  
3. Press @ G.  
4. Enter the values of the variables. The calculation result will be displayed  
after entering the value for all used variables.  
• You can use both global and local variables in your equation, but only  
local variables will be stored if you save the equation. (See page 58.)  
• You need enter only the side of the equation that contains the variables.  
• Performing simulation calculation will cause the variables memories to  
be overwritten with new values.  
• The answer calculated will be stored in last answer memory.  
• To exit simulation calculation, press j.  
Changing a value of variables and editing an expression  
When you are in the solution display, press e to return to the display for  
entering values of variables, then return to the equation display in the  
NORMAL mode by pressing j.  
πRŒH=  
785.3981634  
Solution display  
πRŒH  
H=z  
NORMAL MODE  
πRŒH_  
→
e
→
j
0.  
5.  
Use d u to  
move between  
variables.  
55  
Chapter 3: Scientific Calculations  
Simulate an equation for different values  
Example  
Find the area S = bc sin A ÷ 2 when:  
A
1 b = 3, c = 5 and A = 90° (DEG)  
2 b = 3, c = 5 and A = 45° (DEG)  
3 b = 4, c = 5 and A = 45° (DEG)  
c
b
S
1. Press b0 to select the NORMAL mode.  
2. Press @ J0 0 j.  
• Sets the angular unit to DEG.  
S = bc sin A ÷ 2  
3. Press ; B ; C v  
NORMAL MODE  
; A z2.  
0.  
• The equation is entered in the normal  
way.  
BCsinA©2_  
4. Press @ G.  
BCsinA©2  
A=z  
• The calculator automatically calls the  
display for entering variables and picks  
out the variables in alphabetical order.  
• If a variable already has a value, the  
calculator displays that value automati-  
cally.  
0.  
0.  
•
indicates that there are more variables.  
5. Press 90 e.  
BCsinA©2  
B=z  
• The calculator picks out the next  
variable.  
6. Press 3 e 5.  
BCsinA©2  
C=5_  
•
indicates that this is the last variable.  
7. Press e.  
BCsinA©2=  
7.5  
Area of triangle 1 is 7.5  
square units.  
56  
Chapter 3: Scientific Calculations  
8. Press e and then 45 e.  
2BCsinA©2  
• After getting the answer, press e to  
return to the display for entering  
variables.  
B=z  
3.  
9. Press @ h.  
BCsinA©2=  
• Sides b and c are both the same length  
in triangle 2 as in triangle 1, so you do  
not have to re-enter these values.  
5.303300859  
Area of triangle 2 is  
displayed.  
10. Press e and then d 4 e  
BCsinA©2=  
@ h.  
7.071067812  
Area of triangle 3 is  
displayed.  
57  
Chapter 3: Scientific Calculations  
Filing Equations  
When the calculator is in the NORMAL mode (excluding N-base), you can  
save equations in the EQUATION FILE. Saved equations can be loaded or  
deleted in the NORMAL mode.  
Press f in the NORMAL mode to call the EQUATION FILE menu.  
• Press 0, 1 or 2 to select if an  
equation is to be loaded, saved or deleted,  
respectively.  
<EQTN FILE>  
ƒLOAD ⁄SAVE  
¤DEL  
Saving an equation  
You can save an equation as follows.  
1. After entering an equation in the NORMAL  
mode, press 1 in the EQUATION FILE  
menu.  
SAVE:TITLE?  
• The file name display appears asking you  
to enter a title.  
• The calculator automatically locks ALPHA on to enable you to enter  
alphabetic characters easily. To cancel the ALPHA setting, press ;.  
2. Enter the title of the file (up to seven  
characters).  
SAVE:RING_  
• If you change your mind and no longer  
want to save the equation, press j.  
“RING” is entered as the  
file name.  
3. Press e to save the equation.  
• The display returns to the display before pressing f.  
Note:  
• When saving an equation, local variables (including their values)  
used in the equation are saved at the same time.  
58  
Chapter 3: Scientific Calculations  
Loading and deleting an equation  
The procedures to retrieve (load) and delete an equation from memory are  
the same, except that you have to confirm that you wish to delete the  
equation.  
Retrieve or delete an equation as follows.  
1. Press f and then 0 or 2 to  
DEL ¬º⁄RING  
retrieve (load) or delete.  
º¤AREA-3  
º‹CIRCUIT  
DEL has been selected.  
2. Use d u to select the name of the  
TITLE:RING  
DELETE¬[DEL]  
QUIT¬[ENTER]  
file you wish to retrieve (or delete),and  
press e.  
• The display asks for confirmation if you  
are deleting an equation. Press y to  
proceed with deletion or e to cancel  
the operation.  
Note:  
• If the equation being retrieved contains local variables, the local  
variable names and their values will be retrieved along with the  
equation.  
• Any other equation on the display and local variables before the  
equation was retrieved are cleared.  
59  
60  
Chapter 4:  
Statistical Calculations  
The STAT mode is used to perform statistical calculations.  
Press b 1to select the statistics mode. The seven statistical  
calculations listed below can be performed. After selecting the statistics  
mode, select the desired sub-mode by pressing the number key that  
corresponds to your choice.  
To change statistical sub-mode, reselect statistics mode (press b 1),  
then select the required sub-mode.  
0(SD)  
: Single-variable statistics  
1(LINE)  
2(QUAD)  
3(EXP)  
4(LOG)  
: Linear regression calculation  
: Quadratic regression calculation  
: Exponential regression calculation  
: Logarithmic regression calculation  
5(POWER) : Power regression calculation  
6(INV) : Inverse regression calculation  
61  
Chapter 4: Statistical Calculations  
The following statistics can be obtained for each statistical calculation (refer  
to the table below):  
Variables  
Contents  
Number of samples  
Key operations  
I 00  
I 01  
I 02  
I 03  
I 04  
I 05  
I 06  
I 07  
I 08  
I 09  
I 0A  
I 0B  
I 20  
I 21  
I 22  
I 23  
n
¯x  
Mean of samples (x data)  
sx  
Sample standard deviation (x data)  
Population standard deviation (x data)  
Sum of samples (x data)  
Q
σ
Σ
x
x
Σ
x2  
Sum of squares of samples (x data)  
Mean of samples (y data)  
¯y  
sy  
Sample standard deviation (y data)  
Population standard deviation ( y data)  
Sum of samples (y data)  
σ
Σ
y
y
Σ
Σ
y2  
Sum of squares of samples (y data)  
Sum of products of samples (x, y)  
Coefficient of regression equation  
Coefficient of regression equation  
Coefficient of quadratic regression equation  
Correlation coefficient  
W
xy  
a
b
c
r
• Use I key to perform a STAT variable calculation.  
Single-variable statistical calculation  
Statistics of 1 and value of the normal probability function  
Linear regression calculation  
Statistics of 1 and 2 (except coefficients c) and, in addition, estimate of y  
for a given x (estimate y´) and estimate of x for a given y (estimate x´)  
Exponential regression, logarithmic regression, power  
regression, and inverse regression calculation  
Statistics of 1 and 2 (except coefficients c). In addition, estimate of y for a  
given x (estimate y´) and estimate of x for a given y (estimate x´). (Since the  
calculator converts each formula into a linear regression formula before  
actual calculation takes place, it obtains all statistics, except coefficients a  
and b, from converted data rather than entered data.)  
62  
Chapter 4: Statistical Calculations  
Quadratic regression calculation  
Statistics of 1 and 2 and coefficients a, b, c in the quadratic regression  
2
formula (y = a + bx + cx ). (For quadratic regression calculations, no correla-  
tion coefficient (r) can be obtained.)  
Data Entry and Correction  
All data entered is kept in memory until STAT memory clear (@P  
2y) is operated or a new STAT sub-mode is selected. Before  
entering new data, clear the memory contents.  
Data entry  
Single-variable data  
Data _  
Data , frequency _(To enter multiples of the same data)  
Two-variable data  
Data x , Data y _  
Data x , Data y , frequency _(To enter multiples of the  
same data x and y.)  
• Up to 100 data items can be entered. With single-variable data, a data item  
without frequency assignment is counted as one data item, while an item  
assigned with frequency is stored as a set of two data items. With two-  
variable data, a set of data items without a frequency assignment is  
counted as two data items, while a set of items assigned with frequency is  
stored as a set of three data items.  
Data correction  
Correction prior to pressing _immediately after a data entry:  
Delete incorrect data with j, then enter the correct data.  
63  
Chapter 4: Statistical Calculations  
Correction after pressing _:  
Use udto display the data set previously entered.  
Press dto display the data set in ascending (oldest first) order. To  
reverse the display order to descending (latest first), press the u  
key.  
Each data set is displayed with ‘X=’, ‘Y=’, or ‘N:’ (N is the sequential  
number of the data set).  
Data x  
Frequency  
X=z  
›
75.  
3.  
Data set number  
Data x  
Data y  
Frequency  
X=z  
Y=  
›
4.  
3.  
3.  
Data set number  
Display and move the cursor to the data item to be modified by using  
ud, input the correct value, then press _or e.  
• To delete a data set, display and move the cursor to an item of the  
data set to delete by using ud, then press @#. The  
data set will be deleted.  
• To add a new data set, press j to exit the display of previously  
entered data and input the values, then press _.  
Example  
Key operations  
Result  
Stat 0 [SD]  
b 10  
0.  
DATA  
30  
40  
30  
40  
_
,
DATA SET= 1.  
DATA SET= 2.  
2
_
40  
50  
50  
_
DATA SET= 3.  
DATA  
30  
45  
ddd  
45  
_
X=  
¤
45.  
3.  
45  
3
_
45  
60  
d
60  
_
X=  
60.  
64  
Chapter 4: Statistical Calculations  
Statistical Calculation Formulas  
Type  
Linear  
Exponential  
Logarithmic  
Power  
Regression formula  
y = a + bx  
y = a • ebx  
y = a + b • ln x  
y = a • xb  
1
y = a + b —  
x
Inverse  
Quadratic  
y = a + bx + cx2  
In the statistical calculation formulas, an error will occur if:  
• The absolute value of an intermediate result or calculation result is equal  
to or greater than 1 × 10100  
.
• The denominator is zero.  
• An attempt is made to take the square root of a negative number.  
• No solution exists for a quadratic regression calculation.  
2
2
2
2
Σ
x – nx  
n
x – nx  
Σ
Σ
x
σ
x =  
sx =  
x =  
n
n – 1  
2
2
x = x 2 + x 2 + ··· + x  
Σ
x = x + x + ··· + x  
n
Σ
Σ
1
2
1
2
n
2
2
2
2
y – ny  
n
Σ
y – ny  
Σ
Σ
n
y
y =  
sy =  
σ
y =  
n – 1  
2
2
xy = x y + x y + ··· + x y  
y = y + y + ··· + y  
y = y 2 + y 2 + ··· + y  
Σ
Σ
1 1  
2 2  
n
n
1
2
n
1
2
n
65  
Chapter 4: Statistical Calculations  
Normal Probability Calculations  
• P(t), Q(t), and R(t) will always take positive values, even when t<0,  
because these functions follow the same principle used when solving for  
an area.  
• Values for P(t), Q(t), and R(t) are given to six decimal places.  
–
x – x  
t =  
Standardization conversion formula  
σ
x
66  
Chapter 4: Statistical Calculations  
Statistical Calculations Examples  
Example  
Key operations  
Result  
@P 2y  
Stat 0 [SD]  
b 10  
0.  
DATA  
95  
80  
80  
75  
95_  
DATA SET= 1.  
DATA SET= 2.  
DATA SET= 3.  
DATA SET= 4.  
80_  
_
75,3_  
75  
75  
50  
50_  
DATA SET= 5.  
˛= 75.71428571  
–
x =  
I 01e  
I 03e  
I 00e  
I 04e  
I 05e  
I 02e  
A e  
σ≈= 12.37179148  
σ
x
=
n =  
n=  
7.  
=
=
Σ
x
Í≈=  
Í≈Œ=  
sx  
530.  
41200.  
Σ
x2  
sx =  
sx2 =  
= 13.3630621  
178.5714286  
–
(95–x)  
sx  
(95-I01)  
zI02k10  
+50e  
×10+50=  
64.43210706  
x = 60 →P(t) ?  
I1160I10  
)e  
0.102012  
0.691463  
t = –0.5 →R(t) ?  
I13S0.5)e  
67  
Chapter 4: Statistical Calculations  
Example  
Key operations  
Result  
@P 2y  
DATA  
Stat 1 [LINE]  
b 11  
0.  
x
y
DATA SET= 1.  
DATA SET= 2.  
DATA SET= 3.  
DATA SET= 4.  
2,5_  
_
2
5
5
2
12  
21  
21  
21  
15  
12,24_  
21,40,3_  
24  
40  
40  
40  
25  
15,25_  
DATA SET= 5.  
a
b
r
a
=
=
=
=
=
I 20e  
I 21e  
I 23e  
I 02e  
I 07e  
= 1.050261097  
b
= 1.826044386  
r
= 0.995176343  
sx  
sy  
sx  
=8.541216597  
sy  
=15.67223812  
x=3 → y'=?  
y=46 → x' =?  
3I 25  
46I 24  
6.528394256  
24.61590706  
@P 2y  
DATA  
Stat 2 [QUAD]  
0.  
b 12  
x
y
12  
8
5
23  
15  
41  
13  
2
200  
71  
12,41_  
8,13_  
5,2_  
DATA SET= 1.  
DATA SET= 2.  
DATA SET= 3.  
DATA SET= 4.  
DATA SET= 5.  
23,200_  
15,71_  
a
a
b
c
=
=
=
= 5.357506761  
I 20e  
I 21e  
I 22e  
b
=-3.120289663  
c
= 0.503334057  
x=10 → y'=?  
10I 25  
y
= 24.4880159  
y=22 → x'=?  
22I 24  
≈¡: 9.63201409  
≈™:-3.432772026  
68  
Chapter 5  
Equation Solvers  
Simultaneous Linear Equations  
Simultaneous linear equations with two unknowns (2-VLE) or with three  
unknowns (3-VLE) may be solved using this function.  
1 2-VLE: b 3 0  
a1x + b1y = c1  
a2x + b2y = c2  
a1 b1  
a2 b2  
D =  
D =  
2 3-VLE: b 3 1  
a1x + b1y + c1z = d1  
a1 b1 c1  
a2 b2 c2  
a3 b3 c3  
a2x + b2y + c2z = d2  
a3x + b3y + c3z = d3  
• If the determinant D = 0, an error occurs.  
• If the absolute value of an intermediate result or calculation result is equal  
to or greater than 1 × 10100, an error occurs.  
• The results obtained by this function may include a margin of error.  
Example 1  
2x+3y = 4  
x = ?  
Ò
5x+6y = 7  
y = ?  
det(D) = ?  
1. Press b 3 0 to select 2-  
a⁄z  
b⁄  
c⁄  
0.  
0.  
0.  
VLE of the EQN mode.  
2. Enter the value of each coefficient  
(a1, etc.)  
2 e 3 e 4 e  
5 e 6 e 7  
• Coefficients can be entered using ordinary arithmetic operations.  
• To clear the entered coefficients, press j.  
• Press d or u to move line by line. Press @ d or @  
u to jump to the last or top line.  
69  
Chapter 5: Equation Solvers  
3. After inputting the last coefficient,  
x=  
y=  
D=  
–1.  
2.  
–3.  
press e to solve the 2-VLE.  
• After solving, press e or j to  
return to the coefficient entering display.  
You can use @ h to solve the 2-  
VLE, regardless of the cursor position.  
Example 2  
x+y-z = 9  
x = ?  
6x+6y-z = 17 Ò y = ?  
14x-7y+2z = 42  
z = ?  
det(D) = ?  
1. Press b 3 1 to select 3-  
a⁄z  
b⁄  
c⁄  
0.  
0.  
0.  
VLE of the EQN mode.  
2. Enter the value of each coefficient  
(a1, etc.)  
1 e 1 e S 1 e 9 e  
6 e 6 e S 1 e 17 e  
14 e S 7 e 2 e 42  
• Coefficients can be entered using ordinary arithmetic operations.  
• To clear the entered coefficients, press j.  
• Press d or u to move line by line. Press @ d or @  
u to jump to the last or top line.  
3. After inputting the last coefficient, press e to solve the 3-VLE.  
• Press d to display the det(D).  
• After solving, press e or j to  
return to the coefficient entering display.  
You can use @ h to solve the 3-  
VLE, regardless of the cursor position.  
x= 3.238095238  
y=–1.638095238  
Z=  
–7.4  
D=  
105.  
70  
Chapter 5: Equation Solvers  
Quadratic and Cubic Equation Solvers  
Quadratic (ax2 + bx + c = 0) or cubic (ax3 + bx2 + cx + d = 0) equations may be  
solved using these functions.  
1 Quadratic equation solver (QUAD): b 3 2  
2 Cubic equation solver (CUBIC): b 3 3  
• If there are more than 2 results, the next solution can be displayed.  
• The results obtained by this function may include a margin of error.  
Example 1  
3x2 + 4x – 95 = 0  
→
x = ?  
1. Press b 3 2 to select  
QUAD of the EQN mode.  
a=z  
b=  
c=  
0.  
0.  
0.  
2. Enter the value of each coefficient (a,  
etc.)  
3 e 4 e S 95  
• Coefficients can be entered using ordinary arithmetic operations.  
• To clear the entered coefficients, press j.  
• Press d or u to move line by line.  
3
After inputting the last coefficient,  
press e to solve the quadratic  
equation.  
X⁄  
5.  
X¤–6.333333333  
• After solving, press e or j to  
return to the coefficient entering display.  
You can use @ h to solve the  
quadratic equation, regardless of the cursor position.  
71  
Chapter 5: Equation Solvers  
Example 2  
5x3 + 4x2 +3x + 7 = 0  
→
x = ?  
1. Press b 3 3 to select  
a=z  
b=  
c=  
0.  
0.  
0.  
CUBIC of the EQN mode.  
2. Enter the value of each coefficient (a, etc.)  
5 e 4 e 3 e 7  
• Coefficients can be entered using ordinary arithmetic operations.  
• To clear the entered coefficients, press j.  
• Press d or u to move line by line. Press @ d or @  
u to jump to the last or top line.  
3. After inputting the last coefficient,  
X⁄–1.233600307  
X¤ 0.216800153  
-
press e to solve the cubic  
equation.  
+1.043018296i  
• After solving, press e or j to  
return to the coefficient entering display.  
You can use @ h to solve the  
cubic equation, regardless of the cursor  
position.  
72  
Chapter 6  
Complex Number  
Calculations  
The CPLX mode is used to carry out addition, subtraction, multiplication, and  
division of complex numbers. Press b 4 to select the CPLX mode.  
Results of complex number calculations are expressed in two modes:  
1 @ E: Rectangular coordinates mode (xy appears.)  
2 @ u: Polar coordinates mode (rθ appears.)  
Complex Number Entry  
1 Rectangular coordinates are entered as follows:  
x-coordinate + y-coordinate Q  
or x-coordinate + Q y-coordinate  
2 Polar coordinates are entered as follows:  
r R θ  
r: absolute value  
θ:argument  
• On selecting another mode, the imaginary part of any complex number  
stored in the M memory will be cleared.  
• A complex number expressed in rectangular coordinates with the y-value  
equal to zero, or expressed in polar coordinates with the angle equal to  
zero, is treated as a real number.  
• Press I 0 to return the complex conjugate of the specified complex  
number.  
73  
Chapter 6: Complex Number Calculations  
Example  
Key operations  
Result  
COMPLEX MODE  
b 4  
0.  
8.  
( 12- 6Q ) +  
( 7+ 15Q ) -  
( 11+ 4Q ) e  
(12–6i) + (7+15i) –  
(11+4i) =  
+5.i  
6×(7–9i)×  
(–5+8i) =  
6k ( 7- 9Q )  
k ( S 5 + 8Q  
) e  
222.  
+606.i  
16×(sin30°+  
icos30°)÷(sin60°+  
icos60°)=  
16k ( v 30+  
Q $ 30) z (  
v 60+  
Q $ 60) e  
13.85640646  
+8.i  
@ u 8R 70+ 12  
R 25e  
18.5408873  
42.76427608  
∠
r1 = 8, θ1 = 70°  
r2 = 12, θ2 = 25°  
↓
r = ?, θ = ?°  
(1 + i)  
↓
@ E 1+ Q e  
1.  
+1.i  
@ u  
1.414213562  
r = ?, θ = ?°  
∠
45.  
(2 – 3i)2 =  
@ E ( 2- 3Q  
) A e  
–5.  
–12.i  
( 1+ Q ) @  
Z e  
1
=
1 + i  
0.5  
–0.5i  
I
0 ( 5+ 2  
Q
conj(5+2i) =  
) e  
5.  
–2.i  
74  
Chapter 7  
Programming  
PROG mode  
A program enables you to automate a series of calculations, including those  
simple and complex. Programs are created either in the NORMAL program  
mode or in the NBASE program mode.  
Entering the PROG mode  
1. Press b 2 to select the PROG  
PROGRAM MODE  
ƒRUN ⁄NEW  
¤EDIT ‹DEL  
(PROGRAM) mode.  
2. Press 0 to RUN a program, press  
1 to create a NEW program, press  
2 to EDIT a program, and press 3  
to DELETE a program.  
Selecting the NORMAL program mode or the NBASE  
program mode  
Before creating a new program (b 2 1), select either the  
NORMAL program mode or the NBASE program mode.  
In the NORMAL program mode, you can perform simple mathematical  
calculations and statistical operations. In the NBASE program mode, you can  
perform logical operations and calculations using N-base numbers.  
Programming concept  
It is not within the scope of this manual to describe how to write programs for  
the calculator in detail. Previous programming experience is required to read  
this section. The programming language for this calculator is similar to those  
in general use today.  
All conventional computer and calculator programs use fundamental  
elements such as input, flow control, loops, calculation, and output. The  
programming language in your calculator includes commands that allow you  
to incorporate all of these fundamental elements into your programs. For the  
command list, refer to the ‘Programming Commands.’ (See page 79.)  
Note:  
• Commands must be entered using the COMMAND menu (i). DO  
NOT type commands manually using the ; key.  
75  
Chapter 7: Programming  
Keys and display  
In the PROG mode, to make programs as simple as possible, some keys and  
the display may work in a different manner to other modes. The differences  
are described below.  
• Press i (the f key) to directly access the command menu for  
programming. The Filing Equation function does not work in PROG mode.  
• While entering a program name, keys are locked in ALPHA mode (A-  
LOCK) automatically.  
• In a program, a single line can hold up to 159 letters, where all commands  
are counted as a single letter. As you type in a line, the text will scroll to  
the left. Lines do not wrap in the PROG mode.  
Creating a NEW Program  
After you name the program, the calculator automatically stores the whole  
program under this name as you create it.You do not have to save the  
program manually.  
Creating a NEW program  
1. Press b 2 to enter the PROG mode and then press 1 to  
create a NEW program.  
MODE  
• The display prompts you to select the  
ƒNORMAL ⁄NBASE  
NORMAL program mode or the NBASE  
program mode.  
2. For this example, press 0 to select the  
TITLE? :NORMAL  
SLOPE_ :NORMAL  
NORMAL program mode.  
• The display prompts you to enter a  
program name.  
3. Type the name of the program (i.e.,  
SLOPE).  
• A program name can have up to 7 letters.  
• The calculator automatically switches to  
the alphabet-lock mode.You do not have to press the ; key each  
time before entering an alphabetic character.  
4. After completion, press e.  
SLOPE :NORMAL  
• You are now ready to write a program.  
PROGRAM?  
• Each program line is saved after you  
press u, d or e.  
• You can use the calculator’s regular functions as commands.You can  
also use the additional programming commands in the i menu.  
76  
Chapter 7: Programming  
Use of variables  
Global and local variables are treated differently in the PROG mode.  
• The letters A – Z and θ, used on their own, represent global variables.  
Global variables correspond to the memories of the calculator (e.g., ‘C’ in a  
program means memory C of the calculator). Global variables allow your  
programs to use values stored in memories, or to pass variables from one  
program to another. Global variables also allow you to store results from  
programs and use them in any mode.  
• You can also name and use up to nine local variables (@ v). Local  
variables retain values only in an individual program.  
If a line in your program contains an equation  
such as Y = M1X + 5, it sets the global variable  
Y equal to (M1 × X) + 5. On encountering this  
equation while running the program, if the  
value of the local variable M1 has not been  
defined earlier in the program, the calculator  
prompts you with the display ‘M1=?’ to enter a  
value for M1. The global variable X will already  
be set to the value last stored in that memory.  
SLOPE :NORMAL  
Y=M¡X+5  
_
SLOPE :NORMAL  
M¡=?  
With just a little practice you will soon become  
proficient at typing programs into your calculator.  
Example  
Create a simple program that requests input of the base length (B1)  
and height (H1) of a triangle and then calculates the area (A). After  
creating, RUN the program to determine the area of a triangle with a  
base of 4 units and a height of 3 units.  
1. Preparing to create a NEW program  
Procedure  
Key operations  
Display  
Enter the PROG mode.  
Select NEW.  
b 2  
1
0
Select the NORMAL program mode.  
Type the program name.  
Enter the program name.  
AREA  
AREA :NORMAL  
PROGRAM?  
e
77  
Chapter 7: Programming  
2. Entering the program  
Program code  
Key operations  
i 1 @ v B1 e e @  
Print“B≥=BASE  
a = BASE ; e  
i 1 @ v d H1 e e  
Print“H≥=HEIGHT  
A=1ı2B≥H≥  
@ a = HEIGHT; e  
; A ; =  
1
k
2
@ v  
e @ v d e e  
i 1 @ a AREA ; e  
Print“AREA  
Print A  
i 0 ;  
Ae  
• To enter more than one alphabetic character, press @ a to apply  
the alphabet-lock mode. Press ; to escape from this mode.  
3. Running the program  
Procedure  
Key operations  
Display  
Return to the initial display  
for the PROG mode.  
j
RUN ¬º⁄AREA  
Select and RUN the program.  
0
e
(Select the program.)  
Enter 4 for B1  
Enter 3 for H1  
4e  
AREA  
A=  
3e  
6.  
• If the value of a local variable you defined using @ v is unknown,  
the program automatically prompts you to input a value.  
• To quit running the program, press j. To run the program again, press  
e.  
• When a program is running, text displayed by the program (using the Print”  
command) will wrap to the next line if the text length exceeds the display  
width.  
• You can only enter one command per line except for special cases such as  
the ‘If…Goto’ structure.  
• For more programming examples, see Chapter 8: Application Examples.  
78  
Chapter 7: Programming  
Programming Commands  
In this section, all commands that are available in the PROG mode are  
described, excluding keyboard commands and I menu commands.  
Input and display commands  
1. While creating a NEW or EDIT program,  
<COMMAND-1>  
press i to access the COMMAND  
menu.  
ƒPrint ⁄Print"  
¤Input ‹Wait  
• The first page of the COMMAND menu is  
displayed.  
• Press d or u to scroll page by page.  
• You may directly enter a command by pressing the corresponding  
alphanumeric key without first having to display the relevant COMMAND  
menu page.  
Key  
operations  
Command  
Description  
Examples  
i 0  
Print A  
Displays the value of the  
specified variable. The display  
format is determined by the  
SET UP menu.  
Print  
<variable>  
Print B≥  
Print” SHARP  
Print”  
<text>  
i 1 Displays the text entered after  
the quotation mark. If the text  
exceeds three lines, only the  
last three lines will be displayed.  
Temporarily stops the program  
Input A  
Input  
i 2  
and prompts you to enter a  
value for the variable with the  
display ‘<variable>=?’.  
<variable>  
Input B≥  
i 3  
Pauses the program for the  
specified number of seconds.  
The maximum wait time is 255  
seconds. If no wait time is  
Wait  
<number>  
Wait 5  
Wait FF  
(hexadecimal  
mode)  
specified, the program pauses  
until you press any of the keys.  
The BUSY indicator stays on  
while the program is waiting.  
Wait 1010  
(binary mode)  
79  
Chapter 7: Programming  
Key  
Command  
Description  
Examples  
operations  
Indicates the line is a remark  
and not a command, thus  
allowing you to insert comments  
in the program. Any line  
Rem  
<text>  
Rem TIME TABLE  
i 4  
beginning with Rem is ignored  
when running a program.  
Excessive use of this command  
will use up a considerable  
amount of memory.  
Terminates the program. If the  
program finishes at the last  
command, an End command is  
not required. If there is no End  
command in the program, the  
last calculated answer will be  
displayed when the program  
finishes.  
End  
End  
i 5  
You can use more than one  
End command in the same  
program to terminate after  
different branches, subroutines,  
etc. have been executed.  
80  
Chapter 7: Programming  
Flow control  
Command  
Key  
Description  
Examples  
operations  
Indicates a destination point for  
the flow statements Goto and  
Gosub. Up to seven letters can  
be used for the label name.  
Each label name must be  
unique. You cannot use the  
same label name more than  
once in a program. Up to 20  
different labels can be used in  
each program.  
i 6  
Label  
<label name>  
Label LOOP1  
Label LOOP2  
i 7  
i 8  
Clrt  
Clrt  
Clear the text displayed on the  
screen.  
If B≥=1 Goto  
LOOP1  
If  
The If clause must be followed  
by a conditional statement and  
<condition>  
Goto  
<label name>  
i 9 then a Goto command. Goto is  
the only command allowed to  
be used after the If clause. You  
can enter ; s before  
the Goto command to make the  
line easier to read.  
i 9  
Goto LOOP2  
Gosub PART1  
Goto  
<label name>  
Causes the program to jump to  
the stated Label (specified by a  
Label command). A Goto  
statement must have a  
corresponding Label statement  
line that indicates where to go.  
Runs the subroutine beginning  
at the stated Label (specified by  
a Label command). A Gosub  
statement must have a  
Gosub  
<label name>  
i A  
corresponding subroutine that  
starts after the Label statement  
and ends with a Return  
command. Subroutines can be  
nested up to ten levels deep.  
Return  
Defines the end of a subroutine.  
Operation returns to the  
command following the  
corresponding Gosub  
statement.  
Return  
i B  
81  
Chapter 7: Programming  
Equalities and inequalities  
These expressions are used to form the conditional statement in the If  
clause. They are the basis for looping and other flow control operation in  
programs.  
The ‘=’ (equals) sign is also used as a function to form a substitution  
command for variables.  
You can also enter ‘=’ by simply pressing ; =.  
Key  
operations  
Symbols  
Description  
Examples  
i C  
Equals. This function is also If B=0 Goto ZERO  
=
used to form a substitution  
command that assigns a  
new value to a variable,  
including incrementing or  
decrementing.  
A=A+1  
i D Less than  
If B<0 Goto NGTV  
<
<=  
>=  
>
If B≥<=0 Goto CALC  
i E Less than or equal to.  
i F Greater than or equal to.  
i G Greater than  
If B>=0 Goto RECALC  
If B≥>0 Goto PSTV  
i H Not equal to.  
≠
If A≠B Goto DIF  
82  
Chapter 7: Programming  
Statistical Commands  
In the PROG mode, statistical commands are only available when the  
NORMAL program mode is selected. If the NBASE program mode is  
selected, the statistical command menu cannot be called.  
• When you use the STATx or STATxy commands, the calculator erases all  
data previously stored in the STAT function.  
Key  
operations  
Command  
Description  
Examples  
Selects single-variable  
statistics mode (SD).  
STATx  
STATx  
i I  
Selects linear regression  
calculation mode (LINE).  
STATxy  
STATxy  
i J  
i K  
Enters new statistical data.  
The data format must be  
consistent with the statistics  
mode selected (single-  
variable or linear  
regression). A statistical  
data set entered in the  
PROG mode cannot be  
accessed later for use with  
STAT functions.  
Data  
<x>  
Data 5  
Data  
<x, frequency  
>
Data 25,2  
Data 72,175  
Data 9,96,3  
Data  
<x, y>  
Data  
<
x, y, frequency>  
83  
Chapter 7: Programming  
Editing a Program  
1. Press b 2 to enter the PROG mode and then press 2 to  
select the EDIT mode.  
2. Select the program you wish to edit and press e.  
• If you want to add text into your program, press @ O.  
• If you want to add lines into your program, press @ O (the shape  
of the cursor will become a triangle) and then move the cursor to the  
beginning of the line and press e to add a new line there.  
• Remember that you can enter only one command per line except in the  
special case of the ‘If…Goto’ command. Do not try to enter two or more  
commands on a single line.  
• The line you modify is saved after you press u, d or e. If you  
do not wish to change the line, press j twice. (The line will disap-  
pear at this point, however, the contents of the line are not deleted.)  
• To clear an entire line of a program, press j then u, d or  
e. To delete a blank line, move the cursor to the blank line and press  
y.  
• Any blank lines will be ignored when running.  
• y deletes the character you have just entered (the character at the  
cursor position).  
• You can change the name of a program by overwriting the existing  
name. Press u to move the cursor to the title line and type the new  
name and press e.  
3. Press j to exit the EDIT mode.  
84  
Chapter 7: Programming  
Error Messages  
The calculator displays an error message if a program encounters a problem.  
The error message indicates the nature of the problem while the calculator  
can display the line where the problem has occurred.  
After entering a program, it is often necessary to debug it. To make this task  
easier, the calculator displays an error message if it encounters a problem  
while running your program.  
For example, if you have more than one label  
with the same name in your program, you will  
see the message on the right.  
- ERROR 04 -  
LBL DUPLICATE  
To display the faulty line in the EDIT mode,  
press r or l. To return to the program  
menu, press j.  
You can press j to stop your program at  
any time while it is running. This will be  
necessary if your program enters an endless  
loop.  
BREAK!  
After ‘BREAK!’ is temporarily displayed, the  
initial PROG mode display will reappear. For a list of error messages, refer to  
the Appendix. (See page 120.)  
85  
Chapter 7: Programming  
Deleting Programs  
You can create as many programs as you want within the limitations of the  
calculator’s memory. To free up space for new programs, you must delete old  
ones.  
1. Press b 2 to enter the PROG  
PROGRAM MODE  
ƒRUN ⁄NEW  
¤EDIT ‹DEL  
mode.  
2. Press 3.  
DEL ¬º⁄AREA  
º¤TEMP  
• The delete window appears. All the stored  
programs are listed.  
º‹STAT  
3. Move the cursor to the program you wish  
TITLE:AREA  
DELETE¬[DEL]  
QUIT¬[ENTER]  
to delete and press e.  
• The calculator asks you if you are sure  
you want to delete the program.  
• Press y to delete the program or e  
to cancel this operation.  
86  
Chapter 8  
Application Examples  
Programming Examples  
The following examples demonstrate the basic use of programming  
commands including print, input and flow controls. Use the examples for your  
programming reference.  
Some like it hot (Celsius-Fahrenheit conversion)  
This is a program to convert temperatures from Celsius to Fahrenheit and  
vice versa.  
1. Press b 2 1 0 to open a  
window for creating a NEW program.  
2. Type TEMP for the program title then press  
e.  
• A NEW program called ‘TEMP’ will be  
created.  
TEMP :NORMAL  
PROGRAM?  
3. Enter the program as follows.  
• See ‘*’ below for further explanation.  
Program code  
Key operations  
Label START  
i 6 @ a START ;  
e
Print”(1) C TO F  
Print”(2) F TO C  
Input T  
i 1 ( 1 ) @ a  
s C s TO s F ; e  
i 1 ( 2 ) @ a  
s F s TO s C ; e  
i 2 ; T e  
* Here, the program prompts you  
to choose which type of  
conversion you wish to perform.  
Press 1for “C TO F” and  
2for “F TO C”.  
87  
Chapter 8: Application Examples  
Program code  
Key operations  
If T=1 Goto CTOF  
i 8 ; T ; = 1 ;  
s i 9 @ a CTOF  
; e  
If T=2 Goto FTOC  
i 8 ; T ; = 2 ;  
s i 9 @ a FTOC  
; e  
Goto START  
Label CTOF  
i 9 @ a START ;  
e
i 6 @ a CTOF ;  
e
F=(9©5)C≠+32  
; F ; = ( 9 z 5  
) @ v C0 e e +  
32 e  
* The program automatically  
prompts you to enter a value for  
the local variable C0.  
Print F  
End  
i 0 ; F e  
i 5 e  
Label FTOC  
i 6 @ a FTOC ;  
e
C=(5©9)˚(F≠-32)  
; C ; = ( 5 z 9  
) k ( @ v d F0  
e e - 32 ) e  
* The program automatically  
prompts you to enter a value for  
the local variable F0.  
Print C  
End  
i 0 ; C e  
i 5 e  
Running the program  
4. Press j to return to the PROG mode  
PROGRAM MODE  
ƒRUN ⁄NEW  
¤EDIT ‹DEL  
menu.  
5. Press 0, select the program ‘TEMP’  
and press e.  
• The program prompts you to choose which  
conversion you wish to perform. Then it asks you to enter the tempera-  
ture value.  
88  
Chapter 8: Application Examples  
The Heron Formula  
B
Obtaining the area S of triangle with side  
lengths of A, B and C using the Heron  
Formula which is true for any plane triangle.  
A
S
1. Press b 2 1 0 to open a  
C
window for creating a NEW program.  
S = √ T (T – A) (T – B) (T – C)  
2. Type HERON for the program title then  
A + B + C  
T = —————  
2
press e.  
• A NEW program called ‘HERON’ will be  
created.  
3. Enter the program as follows.  
Program code  
Key operations  
Label START  
i 6 @ a START ;  
e
Print”SIDE LENGTHS  
i 1 @ a SIDE s  
LENGTHS ; e  
Input A  
i 2 ; A e  
i 2 ; B e  
i 2 ; C e  
Input B  
Input C  
If (A+B)<=C Goto ERROR  
i 8 ( ; A + ; B  
) i E ; C ; s  
i 9 @ a ERROR ;  
e
If (B+C)<=A Goto ERROR  
If (C+A)<=B Goto ERROR  
T=(A+B+C)©2  
i 8 ( ; B + ; C  
) i E ; A ; s  
i 9 @ a ERROR ;  
e
i 8 ( ; C + ; A  
) i E ; B ; s  
i 9 @ a ERROR ;  
e
; T ; = ( ; A +  
; B + ; C ) z 2  
e
89  
Chapter 8: Application Examples  
Program code  
Key operation  
S=‰(T(T-A)(T-B)(T-C))  
; S ; = @ * (  
; T ( ; T - ; A  
) ( ; T - ; B )  
( ; T - ; C ) )  
e
Print S  
End  
i 0 ; S e  
i 5 e  
Label ERROR  
i 6 @ a ERROR ;  
e
Print”NO TRIANGLE  
i 1 @ a NO s  
TRIANGLE ; e  
Wait 1  
i 3 1 e  
Print”REENTER  
i 1 @ a REENTER ;  
e
Goto START  
i 9 @ a START ;  
e
Example  
Obtain the area of the triangle with the side lengths of 20 cm (A), 35 cm (B)  
and 40 cm (C).  
4. Press j to return to the PROG mode menu.  
5. Press 0, select the program ‘HERON’  
HERON :NORMAL  
SIDE LENGTHS  
A=?  
and press e.  
• If the values you enter do not satisfy the  
conditions to make a triangle (e.g. A + B >  
C where A, B, C are the side lengths), the program prompts you to re-  
enter the values from the beginning. If you wish to stop the program,  
press j.  
6. Enter 20 for A, 35 for B and 40 for C.  
Result  
The area of the triangle is approximately 350  
cm2.  
40  
S=  
349.944192  
90  
Chapter 8: Application Examples  
2B or not 2B (N-base conversion)  
The conversion functions and logical operations can be used in the NBASE  
program mode. The following is a simple program that converts a decimal  
number to binary, pental, octal and hexadecimal formats.  
1. Press b 2 1 1 to open a  
NBASE :NBASE  
PROGRAM?  
window for creating a NEW program in  
the NBASE program mode.  
2. Type NBASE for the title then press e.  
• A NEW program called ‘NBASE’ will be created.  
3. Enter the program as follows.  
Program code  
Print”ENTER A  
Key operations  
i 1 @ a ENTER s A  
; e  
Print”DECIMAL NUMBER  
i 1 @ a DECIMAL s  
NUMBER ; e  
Input Y  
i 2 ; Y e  
Y¬BIN  
; Y @ z e  
Print”BINARY  
i 1 @ a BINARY ;  
e
Print Y  
Wait  
i 0 ; Y e  
i 3 e  
Y¬PEN  
; Y @ r e  
Print”PENTAL  
i 1 @ a PENTAL ;  
e
Print Y  
Wait  
i 0 ; Y e  
i 3 e  
91  
Chapter 8: Application Examples  
Program code  
Key operations  
Y¬OCT  
; Y @ g e  
Print”OCTAL  
i 1 @ a OCTAL ;  
e
Print Y  
i 0 ; Y e  
i 3 e  
Wait  
Y¬HEX  
; Y @ h e  
Print”HEXADECIMAL  
i 1 @ a HEXADECIMAL  
; e  
Print Y  
i 0 ; Y e  
Running the program  
4. Press j to return to the PROG mode menu.  
5. Press 0, select the program ‘NBASE’ and press e.  
• The program prompts you to enter a decimal number and then displays  
it in binary format.  
• Press any key to display the number in pental format, then press any  
key to see it in octal format, and again press any key to see it in  
hexadecimal format.  
• Be careful when using the Wait command in NBASE program mode.  
Numbers followed by Wait are processed according to the current  
number base, binary, pental, octal, decimal or hexadecimal.  
To specify the wait time in decimal format, define a variable (e.g., T = 5)  
for the wait time beforehand and use it in the Wait command (i.e., Wait  
T).  
92  
Chapter 8: Application Examples  
T test  
The T-test value is obtained by comparing the mean values of sample data  
and expected average from sample data. Using the t- distribution table, the  
reliability of a mean value can be evaluated.  
–
x – m  
t = ———  
sx2  
——  
n
m = expected mean value estimated by sample data  
n = the number of samples  
–
x = actual mean value of the samples  
sx = standard deviation of the samples  
Example  
A’s SHOP sells cookies by package on which it is stated contents are 100 g.  
Buy 6 sample packages and check if the statement is true.  
• Setting an expected mean value as 100 (m = 100 g), a t-test value is  
obtained. If it is larger than the expected t-value obtained from a t-  
distribution table (at 5% of risk rate), the estimation is wrong. (In this  
case, A’s SHOP does not sell honestly.)  
Sample  
grams  
1
2
3
4
5
6
102  
95  
107  
93  
110  
98  
1. Press b 2 10 to open a window for creating a NEW program.  
2. Type TTEST for the title then press e.  
• A NEW program called ‘TTEST’ will be created.  
3. Enter the program as follows.  
93  
Chapter 8: Application Examples  
Program code  
Key operations  
i I e  
STATx  
Data 102  
Data 95  
i K 102 e  
i K 95 e  
Data 107  
Data 93  
i K 107 e  
i K 93 e  
Data 110  
Data 98  
i K 110 e  
i K 98 e  
Print”MEAN  
Input M  
i 1 @ a MEAN ; e  
i 2 ; M e  
T=(˛-M)©‰(sxŒ©˜)  
; T ; = ( I 5  
1 - ; M ) z @  
* ( I 5 2 A z  
I 5 0 ) e  
Print T  
End  
i 0 ; T e  
i 5 e  
Running the program  
4. Press j to return to the PROG mode menu.  
5. Press 0, select the program ‘TTEST’ and press e.  
6. Enter the expected mean value ‘100’ and press e.  
T=  
0.303058133  
Result  
The t-test value of 0.303 is smaller than the 2.571, expected mean value  
obtained from a t-test distribution table (at 5% of risk rate), showing that  
they sell honestly.  
94  
Chapter 8: Application Examples  
A circle that passes through 3 points  
When three different points, P (X1, Y1), Q (X2, Y2), S (X3, Y3) are given,  
obtain the center coordinates O (X, Y) and the radius R of the circle that  
passes through these points.  
Q (X2, Y2  
)
To satisfy the above conditions, the  
distances between P, Q, S and O  
should be equal. as they are the  
radius of the same circle. Therefore,  
R
P (X1, Y1  
1–Y  
)
R
Y
O (X, Y)  
X
1–X  
PO = QO = SO = R  
R
Using the Pythagorean theorem,  
2
2
PO = X1 – X + Y1 – Y 2 = R2  
(
(
(
)
(
(
(
)
)
)
S (X3, Y3  
)
2
2
QO = X2 – X + Y2 – Y 2 = R2  
)
2
2
SO = X3 – X + Y3 – Y 2 = R2  
)
then  
(X12+Y12-X22-Y22)(Y2–Y3) – (X22+Y22-X32-Y32)(Y1–Y2  
2{(X1–X2)(Y2–Y3) – (X2–X3)(Y1–Y2)}  
)
X =  
Y =  
------ 1  
------ 2  
------ 3  
(X12+Y12-X22-Y22)(X2–X3) – (X22+Y22-X32-Y32)(X1–X2  
)
2{(Y1–Y2)(X2–X3) – (Y2–Y3)(X1–X2)}  
2
R = (X – X1)2 + (Y – Y1  
)
To enhance both readability and writability of the program, intermediate  
variables G, H, I, J, K and M are used.  
The above equations reduce to  
GM – HK  
2 (IM – JK)  
GJ – HI  
2 (KJ – MI)  
X =  
Y =  
1. Press b 2 10 to open a window for creating a NEW program.  
2. Type CIRCLE for the title then press e.  
• A NEW program called ‘CIRCLE’ will be created.  
3. Enter the program as follows.  
Program code  
Key operations  
Print”ENTER COORDS  
i 1 @ a ENTER s COORDS  
; e  
G=X≥Œ+Y≥Œ-X√Œ-Y√Œ  
; G ; = @ v X1 e  
e A + @ v d Y1 e  
e A - @ v d d X2  
e e A - @ v d  
d d Y2 e e A e  
* Calculate intermediate  
values.  
95  
Chapter 8: Application Examples  
Program code  
Key operations  
H=X√Œ+Y√Œ-X…Œ-Y…Œ  
; H ; = @ v 2 A  
+ @ v 3 A - @ v  
d d d d X3 e e A  
- @ v d d d d d  
Y3 e e A e  
I=X≥-X√  
J=X√-X…  
K=Y≥-Y√  
M=Y√-Y…  
; I ; = @ v 0 -  
@ v 2 e  
; J ; = @ v 2 -  
@ v 4 e  
; K ; = @ v 1 -  
@ v 3 e  
; M ; = @ v 3 -  
@ v 5 e  
X=(GM-HK)©2(IM-JK)  
; X ; = ( ; G ; M -  
; H ; K ) z 2 ( ; I  
; M - ; J ; K ) e  
* Perform equation 1.  
Print X  
i 0 ; X e  
Wait  
i 3 e  
Y=(GJ-HI)©2(KJ-MI)  
; Y ; = ( ; G ; J -  
; H ; I ) z 2 ( ; K  
; J - ; M ; I ) e  
* Perform equation 2.  
Print Y  
Wait  
i 0 ; Y e  
i 3 e  
R=‰((X-X≥)Œ+(Y-Y≥)Œ) ; R ; = @ * ( ( ; X  
- @ v 0 ) A + ( ;  
* Perform equation 3.  
Y - @ v 1 ) A ) e  
Print R  
i 0 ; R e  
Example  
Obtain the center coordinates (X, Y) and radius R of the circle that passes  
through points P(1, 9), Q (7, 1) and S (0, 2).  
4. Press j to return to the PROG mode menu.  
5. Press 0, select the program ‘CIRCLE’ and press e.  
6. Enter the coordinates (X1 to X3, Y1 to Y3) for the three points.  
Result  
The center is (4, 5) and radius is 5.  
96  
Chapter 8: Application Examples  
Radioactive decay  
Carbon-14 (14C) is a naturally occurring radioactive isotope of carbon used in  
the carbon dating process. Because carbon-14 decays at a steady rate, it is  
possible to determine the age of a once living specimen by measuring the  
residual amount of 14C it contains.  
The mass of 14C contained in a sample changes according to the  
equation  
M
1
–ln ( ––– )  
M
0
M = M0 e–kt or t = –––––––––  
k
where M1 = Mass of 14C at time t  
M0  
= Original mass of 14  
C
k = Radioactive decay constant (for 14C, k = 1.2118 × 10–4 year–1  
)
t = Elapsed time in years  
Example  
This program asks for a original mass and current mass of 14C and tells you  
how old the specimen is. It then finds the half-life of 14C.  
1. Press b 2 1 0 to open a window for creating a NEW  
program.  
2. Type DECAY for the title then press  
DECAY :NORMAL  
PROGRAM?  
e.  
• A NEW program called ‘DECAY’ will be  
created.  
3. Enter the program as follows.  
Program code  
Key operations  
Print”ORIGINAL MASS  
i 1 @ a ORIGINAL s  
MASS ; e  
Input M≠  
i 2 @ v M0 e e  
e
Print”CURRENT MASS  
Input M≥  
i 1 @ a CURRENT s  
MASS ; e  
i 2 @ v d M1 e  
e e  
97  
Chapter 8: Application Examples  
Program code  
Key operations  
T=-(ln(M≥©M≠))©  
1.2118œ-4  
; T ; = S ( i  
( @ v 1 z @  
v 0 ) ) z 1.2118  
` S 4 e  
Print T  
i 0 ; T e  
Print”YEARS  
i 1 @ a YEARS ;  
e
End  
i 5 e  
• The half-life of a radioactive isotope is the time required for half of its  
mass to decay.  
Running the program  
4. Press j to return to the PROG mode menu.  
5. Press 0, select the program  
DECAY :NORMAL  
ORIGINAL MASS  
Mº=?  
‘DECAY’ and press e.  
6. Enter 100 for M0 and 50 for M1.  
Result  
T=  
The half-life of 14C is 5719.980034 years.  
5719.980034  
YEARS  
98  
Chapter 8: Application Examples  
Delta-Y impedance circuit transformation  
Transformation of a Y impedance circuit to an equivalent Delta impedance  
circuit and vice versa.  
The Delta-Y transformation is defined by the following formula:  
Z
2
R
1
R
2
Z
3
Z
1
R
Z
1
Z2  
Z1  
Z2  
Z3  
= —  
R
R
R
1
2
3
= ———  
R2  
Z
2
R
3
R
Z
Z3  
= —  
= ———  
R3  
Z
3
R
Z
Z1  
= —  
= ———  
R1  
Z
where R = R1  
R
2
+ R2R  
3
+ R3R  
1
where Z = Z1 + Z2 + Z3  
1. Press b 2 1 0 to open a window for creating a NEW  
program.  
2. Type DELTAY for the title then press e.  
• A NEW program called ‘DELTAY’ will be created.  
3. Enter the program as follows.  
Program code  
Key operations  
Print”(1)DELTA TO Y  
i 1 ( 1 ) @ a  
DELTA s TO s Y ; e  
Print”(2)Y TO DELTA  
i 1 ( 2 ) @ a Y  
s TO s DELTA ; e  
Input X  
i 2 ; X e  
If X=1 Goto DTOY  
i 8 ; X ; = 1 ;  
s i 9 @ a DTOY  
; e  
If X=2 Goto YTOD  
Label DTOY  
i 8 ; X ; = 2 ;  
s i 9 @ a YTOD  
; e  
i 6 @ a DTOY ;  
e
99  
Chapter 8: Application Examples  
Program code  
Key operations  
Z=Z≥+Z√+Z…  
; Z ; = @ v Z1  
e e + @ v d Z2  
e e + @ v d  
d Z3 e e e  
R≥=Z≥Z√©Z  
@ v d d d R1 e  
e ; = @ v 0  
@ v 1 z ; Z e  
Print R≥  
Wait  
i 0 @ v 3 e  
i 3 e  
R√=Z√Z…©Z  
@ v d d d d R2  
e e ; = @ v  
1 @ v 2 z ; Z  
e
Print R√  
Wait  
i 0 @ v 4 e  
i 3 e  
R…=Z…Z≥©Z  
@ v d d d d  
d R3 e e ; = @  
v 2 @ v 0 z  
; Z e  
Print R…  
End  
i 0 @ v 5 e  
i 5 e  
Label YTOD  
i 6 @ a YTOD ;  
e
R=R≥R√+R√R…+R…R≥  
; R ; = @ v 3  
@ v 4 + @ v  
4 @ v 5 + @  
v 5 @ v 3 e  
Z≥=R©R√  
@ v 0 ; = ; R  
z @ v 4 e  
Print Z≥  
i 0 @ v 0 e  
100  
Chapter 8: Application Examples  
Program code  
Key operations  
Wait  
i 3 e  
Z√=R©R…  
@ v 1 ; = ; R  
z @ v 5 e  
Print Z√  
Wait  
i 0 @ v 1 e  
i 3 e  
Z…=R©R≥  
@ v 2 ; = ; R  
z @ v 3 e  
Print Z…  
End  
i 0 @ v 2 e  
i 5 e  
Example  
When the impedances Z1, Z2, Z3 of a delta impedance circuit are 70, 35,  
140 respectively, obtain the impedances R1, R2, R3 of a Y circuit.  
4. Press j to return to the PROG mode menu.  
5. Press 0, select the program ‘DELTAY’  
(1)DELTA TO Y  
(2)Y TO DELTA  
X=?  
and press e.  
The direction of transformation will be  
asked.  
6. Press 1 e to select ‘DELTA TO Y’ transformation.  
7. Enter 70 for Z1, 35 for Z2 and 140 for Z3.  
Result  
The impedances R1, R2, R3 of the targeted Y impedance circuit are 10, 20  
and 40, respectively.  
101  
Chapter 8: Application Examples  
Obtaining tensions of strings  
Suppose a bar is hung from the ceiling by two strings such that it balances  
with angles the strings make from the perpendicular lines A and B. If the  
weight of the bar is W, obtain the tensions in the strings S and T.  
S
T
W
—— = —— = —————  
Perpendicular  
line  
T
sin A sin B sin (A + B)  
sin B  
T = W —————  
sin (A + B)  
A
B
G
sin A  
S = W —————  
sin (A + B)  
S
where W: weight  
T, S: tension in strings  
A, B: angles that strings make  
from perpendicular lines  
(DMS)  
B
W
S
W
A
T
G:  
gravity  
1. Press b 2 1 0 to open a window for creating a NEW  
program.  
2. Type TENSION for the title then press e.  
• A NEW program called ‘TENSION’ will be created.  
3. Enter the program as follows.  
Program code  
Print“ANGLES  
Key operations  
i 1 @ a ANGLES ;  
e
Input A  
i 2 ; A e  
Input B  
i 2 ; B e  
Print”WEIGHT  
i 1 @ a WEIGHT ;  
e
Input W  
C=AΩDEG  
i 2 ; W e  
; C ; = ; A @ :  
e
D=BΩDEG  
; D ; = ; B @ :  
e
102  
Chapter 8: Application Examples  
Program code  
E=sin(C+D)  
Key operations  
; E ; = v ( ; C  
+ ; D ) e  
S=W ˚ sin C©E  
T=W ˚ sin D©E  
Print”TENSIONS  
@ a S = W ; k v  
; C z ; E e  
@ a T = W ; k v  
; D z ; E e  
i 1 @ a TENSIONS ;  
e
Print S  
Wait  
i 0 ; S e  
i 3 e  
Print T  
End  
i 0 ; T e  
i 5 e  
Example  
Calculate the tension in the strings S and T when the weight of the bar is  
40 kg, angle A: 30° 15' 20" and angle B: 27° 45' 40".  
4. Press j @ J 0 0 to set the angular unit to DEG,  
then @ J 1 0 3 to set display to fixed mode with the  
decimal point of 3 .  
• In this program input angles by degree/minute/second format. They will  
be automatically converted to decimal degrees.  
5. Press b 2 0, select the program ‘TENSION’ and press  
e.  
6. Enter 30 [ 15 [20 for angle A and press e.  
7. Enter 27 [ 45 [40 for angle B and press e.  
8. Enter 40 for weight W and press e for S.  
9. Press e for T.  
Results  
Tension in the strings S and T are 23.761 kg  
and 21.966 kg, respectively.  
23.761  
21.966  
T=  
103  
Chapter 8: Application Examples  
Purchasing with payment in n-month installments  
If you wish to buy goods with the price of P by n-month installments, this  
program determines the payment per month.  
i
S = (P – D) —————  
1 – (1 + i)–n  
where S: payment due every month  
P: price of the product  
n : n-month installment  
D: down payment  
i: installment payment interest rate (%)  
1. Press b 2 1 0 to open a window for creating a NEW  
program.  
2. Type PAYBYMN for the title then press e.  
• A NEW program called ‘PAYBYMN’ will be created.  
3. Enter the program as follows.  
Program code  
Print”PRICE  
Key operations  
i 1 @ a PRICE ;  
e
Input P  
i 2 ; P e  
Print”DOWN PAYMENT  
i 1 @ a DOWN s  
PAYMENT ; e  
Input D  
i 2 ; D e  
Print”MONTHS  
i 1 @ a MONTHS ;  
e
Input N  
i 2 ; N e  
Print”RATE  
i 1 @ a RATE ;  
e
Input I  
I=I©100  
i 2 ; I e  
; I ; = ; I z 100  
e
S=(P-D)˚I©(1-(1+I)^(-N)) ; S ; = ( ; P -  
; D ) k ; I z ( 1  
- ( 1 + ; I ) m  
( S ; N ) ) e  
104  
Chapter 8: Application Examples  
Program code  
Print S  
Key operation  
i 0 ; S e  
Example  
If you wish to buy furniture costing $3,000 with $500 as a down payment  
and pay the remainder in 11 month’s installments with a monthly interest  
rate of 1%, how much is the monthly payment?  
4. Press j to return to the PROG mode menu.  
5. Press 0, select the program  
PAYBYMN:NORMAL  
PRICE  
P=?  
‘PAYBYMN’ and press e.  
6. Enter 3000 for P, 500 for D, 11 for N and 1 for I.  
Result  
Your monthly payment is approx. $241.  
1
S=  
241.1351893  
105  
Chapter 8: Application Examples  
Digital dice  
This program simulates rolling of multiple dice. You can  
play a dice game without dice or where there is not  
enough space to roll dice.  
At the first stage, ask the number of dice to use for play. Secondly, roll dice  
and display the result and wait until any key is pressed.  
1. Press b 2 1 0 to open a window for creating a NEW program.  
2. Type DICE for the title then press e.  
• A NEW program called ‘DICE’ will be created.  
3. Enter the program as follows.  
Program code  
Key operations  
Print”NO OF DICE  
i 1 @ a NO s OF  
s DICE ; e  
Input N  
Label PLAY  
M=1  
i 2 ; N e  
i 6 @ a PLAY ; e  
; M ; = 1 e  
X=0  
; X ; = 0 e  
Label ROLL  
X=X+r.dice  
i 6 @ a ROLL ; e  
; X ; = ; X + @  
w 1 e  
M=M+1  
; M ; = ; M + 1 e  
If M<=N Goto ROLL  
i 8 ; M i E ; N  
; s i 9 @ a  
ROLL ; e  
Print X  
Wait  
i 0 ; X e  
i 3 e  
Goto PLAY  
i 9 @ a PLAY ; e  
Running the program  
4. Press j to return to the PROG mode menu.  
5. Press 0, select the program ‘DICE’ and press e.  
6. Enter the number of dice to play and press e.  
7. Press e (or any other key) to continue to play. Press j to quit.  
106  
Chapter 8: Application Examples  
How many digits can you remember?  
The calculator displays randomly created numbers with the number of digits  
(up to 9) you specified for the number of seconds you entered and asks you  
to enter the number you remembered. After 10 tries the score is displayed.  
The larger the number of digits and the shorter the seconds, the higher the  
score is.  
1. Press b 2 1 0 to open a window for creating a NEW  
program.  
2. Type NUMBER for the title then press e.  
• A NEW program called ‘NUMBER’ will be created.  
3. Enter the program as follows.  
Program code  
Key operations  
M=1  
A=0  
; M ; = 1 e  
; A ; = 0 e  
Print”HOW MANY DIGITS  
i 1 @ a HOW s MANY  
s DIGITS ; e  
Label NINE  
i 6 @ a NINE ; e  
Print”LESS THAN 9 DIGITS i 1 @ a LESS s  
THAN s ; 9 @ a s  
DIGITS ; e  
Input N  
i 2 ; N e  
If N>9 Goto NINE  
i 8 ; N i G 9 ;  
s i 9 @ a NINE  
; e  
Print”HOW LONG  
i 1 @ a HOW s LONG  
; e  
Input T  
i 2 ; T e  
Label QUESTION  
i 6 @ a QUESTION ;  
e
Label AGAIN  
i 6 @ a AGAIN ; e  
S=ipart(random˚10^3)  
; S ; = I 1 (  
@ w 0 k @ Y 3  
) e  
107  
Chapter 8: Application Examples  
Program code  
Key operations  
If S<100 Goto AGAIN  
i 8 ; S i D 100  
; s i 9 @ a  
AGAIN ; e  
S=S˚10^(-3)  
; S ; = ; S k @  
Y ( S 3 ) e  
If N>6 Goto SIX  
i 8 ; N i G 6 ;  
s i 9 @ a SIX ;  
e
If N>3 Goto THREE  
Q=ipart(Sx10^N)  
i 8 ; N i G 3 ;  
s i 9 @ a THREE  
; e  
; Q ; = I 1 (  
; S k @ Y ; N )  
e
Goto DISPLAY  
Label SIX  
i 9 @ a DISPLAY ;  
e
i 6 @ a SIX ; e  
; Q ; = I 1 (  
; S k @ Y ( ; N  
- 6 ) ) k @ Y 6  
+ @ w 0 k @  
Y 6 + @ w 0 k  
@ Y 3 e  
Q=ipart(S˚10^(N-6))˚10^6  
+random˚10^6+random˚10^3  
Goto DISPLAY  
Label THREE  
i 9 @ a DISPLAY ;  
e
i 6 @ a THREE ; e  
; Q ; = I 1 (  
; S k @ Y ( ; N  
- 3 ) ) k @ Y 3  
+ @ w 0 k @  
Y 3 e  
Q=ipart(S˚10^(N-3))˚10^3  
+random˚10^3  
Label DISPLAY  
i 6 @ a DISPLAY ;  
e
Clrt  
i 7 e  
Print Q  
i 0 ; Q e  
108  
Chapter 8: Application Examples  
Program code  
Wait T  
Key operations  
i 3 ; T e  
Clrt  
i 7 e  
Print”ANSWER  
i 1 @ a ANSWER ;  
e
Input X  
i 2 ; X e  
* If answer is correct, add (30 x  
number of digits / number of  
seconds) to score.  
If X Q Goto WRONG  
A=A+int(10˚N©T˚3)  
Label WRONG  
i 8 ; X i H ; Q  
; s i 9 @ a WRONG  
; e  
; A ; = ; A + I  
2 ( 10 k ; N z  
; T k 3 ) e  
i 6 @ a WRONG ;  
e
M=M+1  
; M ; = ; M + 1 e  
If M<=10 Goto QUESTION  
i 8 ; M i E 10  
;
s
i 9 @ a QUESTION  
; e  
Print”YOUR SCORE IS  
i 1 @ a YOUR s  
SCORE s IS ; e  
Print A  
End  
i 0 ; A e  
i 5 e  
Running the program  
4. Press j to return to the PROG mode menu.  
5. Press 0, select the program ‘NUMBER’ and press e.  
6. Enter the number of digits you wish to play with N.  
7. Enter the number of seconds to display the numbers.  
8. Immediately after you press e, the game will start.  
9. After ‘ANSWER X=?’ is displayed, enter the number you remembered  
and press e. After 10 tries, the score is displayed.  
109  
Chapter 8: Application Examples  
Calculation Examples  
Geosynchronous orbits  
The orbit of a satellite about the Earth is  
geosynchronous if the period of the orbit matches  
the period of the Earth’s rotation. At what distance  
from the center of the Earth can geosynchronous  
orbit occur?  
The period of an orbit is described by the equation  
4π2  
T2 = —— r3  
GM  
where T = period of orbit  
G = Gravitational constant (6.6742 × 10–11 m3 kg–1 –2  
)
s
M = Mass of the Earth (5.976 × 1024 kg)  
r = Distance between the satellite and the center of the Earth (radius of orbit)  
The Earth rotates once every 23 hours, 56 minutes and 4.09 seconds. At  
first, convert this time into seconds.  
1. Press b 0 23 [ 56 [ 4.09  
23∂56∂4.09∂Ωse  
[ I 6.  
c
• Determining the value of T.  
86164.09  
2. Press xT to store the result as global  
variable T.  
3. Press @ J 1 1 4.  
• Select the scientific display format with  
four significant digits.  
86164.09  
AnsÒT  
8.616  
• Use the solver function to solve the  
equation for r.  
4. Press j;T A; =  
( 4 @ s A ) z (  
;G ;M )k;R 1.  
0.000  
TŒ=(4πŒ)©(GM)˚  
R„_  
5. Check the equation on the display and  
press I 5 to enter the solver  
function.  
TŒ=(4πŒ)©(GM)˚  
R„  
G=z  
0.000  
110  
Chapter 8: Application Examples  
6. Press @ c 02 e 5.976 ` 24  
TŒ=(4πŒ)©(GM)˚  
R„  
e.  
• Use the physical constants function for the  
G value.  
R=z  
0.000  
• After completion of entering values for variables G and M, the cursor  
moves on to variable R. (The variable T has already its value.)  
7. Press @ h.  
Result  
Geosynchronous orbit is possible approxi-  
R=  
R¬  
L¬  
4.217  
7.424  
7.424  
mately 42,170 km (4.217 × 107 meters) from  
the center of the Earth.  
Twinkle, twinkle, little star (Apparent magnitude of stars)  
The apparent magnitude of a star is a  
measure of how bright it appears. It is a  
function of how far away the star is and  
the luminosity of the star.  
Since stars are seen from different  
distances, their luminosities must be  
standardized before they can be  
compared. This is done using a quantity called the absolute magnitude,  
which is a measure of how bright that star would appear if it was viewed from  
a distance of 10 parsecs (about 32.6 light years).  
If the absolute magnitude of two stars is known, the ratio of their luminosities  
is given by the equation.  
L
2
Log —— = 0.4 (M1 – M2  
)
L1  
where M1 = Absolute magnitude of the first star  
= Absolute magnitude of the second star  
M
2
L
L
1
= Luminosity of the first star  
= Luminosity of the second star  
2
111  
Chapter 8: Application Examples  
Example 1  
What is the ratio of the sun’s luminosity to that of a star having an absolute  
magnitude of 2.89?  
(The sun’s absolute magnitude is 4.8.)  
The former equation is equivalent to  
L
L
2
1
– M2)  
—— = 10 0.4 (M  
1
whereꢀM2 = 2.89  
1. Press b 0 and @ P 0.  
2. Press @ Y ( 0.4 k (  
1
^(0.4˚(4.8-2.  
4.8 - 2.89 ) ) e.  
Î
89))=  
5.807644175  
Result  
5.807644175  
The star is nearly six times as luminous as the sun.  
Example 2  
A second star has only 0.0003 times the luminosity of the sun. What is its  
absolute magnitude?  
The previous equation is equivalent to  
L
2
log ——  
L
0.4  
1
M
2
= M1 – ————  
L
L
2
whereꢀ —— = 0.0003  
1
1. Press 4.8 - ( l 0.0003 z 0.4 )e.  
Result  
The absolute magnitude of the second star is  
approximately 13.6.  
4.8-(log0.0003  
©0.4)=  
13.60719686  
112  
Chapter 8: Application Examples  
Memory calculations  
When you want to use the calculator for tasks such as adding up total sales,  
you can perform this type of operation using single-variable statistics.  
Example  
In one week, an electrical store sold the items listed below at the prices  
and in the quantities shown. What was the total sales figure?  
Item  
Price  
Quantity  
TV set  
$599.95  
10  
Phone  
Clock  
$159.95  
$39.95  
$7.95  
27  
52  
Calculator  
108  
1. Press b 1 0 to select the single-variable statistics mode.  
2. Press 599.95 , 10 _, 159.95  
DATA SET= 3.  
7.95,108DATA  
DATA SET= 4.  
, 27 _, 39.95 , 52 _ and  
7.95 , 108 _.  
• All the data is entered.  
3. Press I 0 4 e.  
• The calculator displays Σx, that is the total  
DATA SET= 4.  
Í≈=  
sales value.  
13254.15  
Result  
■
Total sales were $13254.15.  
113  
Chapter 8: Application Examples  
The state lottery  
Example  
The state you live in has two different numbers lotteries. In the first, you  
must pick 6 numbers between 1 and 50 in any order. In the second, you  
have to pick 5 numbers between 1 and 35, but you must pick them in the  
correct order. Which lottery gives you the better chance of winning?  
In the first lottery, your chances of winning with one ticket are one in 50C6:  
1. Press b 0 50 @ N 6 e.  
0.  
50Ç6=  
15890700.  
Your chances of winning the second lottery with one ticket are one in  
35P5:  
2. Press 35 @ e 5 e.  
15890700.  
35∏5=  
38955840.  
Result  
■
Your chances are better in the first lottery.  
114  
Appendix  
Battery Replacement  
Batteries used  
• Use only the specified batteries.  
Type  
Model  
Quantity  
Lithium battery  
CR2032  
2
• Be sure to write down any important data stored in the memory  
before replacing the batteries.  
Notes on battery replacement  
Improper handling of batteries can cause electrolyte leakage or explosion.  
Be sure to observe the following handling rules:  
• Do not mix new and old batteries.  
• Make sure the new batteries are the correct type.  
• When installing, orient each battery correctly as indicated in the calculator.  
• Batteries are factory-installed before shipment, so may become exhausted  
before reaching the service life stated in the specifications.  
When to replace the batteries  
Replace the batteries immediately when any of the following situations  
occur:  
• The calculator does not turn on when j is pressed.  
• The message ‘Change Batteries’ appears.  
• Continued use of the calculator when in low battery status may  
result in the memory contents being cleared.  
• Executing programs under low battery condition may result in the  
memory contents being cleared.  
• Failure to follow the battery replacement procedure as described  
may result in the memory contents being cleared.  
115  
Appendix  
Cautions  
• Fluid from a leaking battery accidentally entering an eye could result in  
serious injury. Should this occur, wash with clean water and immediately  
consult a doctor.  
• Should fluid from a leaking battery come in contact with your skin or  
clothes, immediately wash with clean water.  
• If the product is not to be used for some time, to avoid damage to the unit  
from leaking batteries, remove them and store in a safe place.  
• Do not leave exhausted batteries inside the product.  
• Do not fit partially used batteries, and be sure not to mix batteries of  
different types.  
• Keep batteries out of the reach of the children.  
• Exhausted batteries left in the calculator may leak and damage the  
calculator.  
• Explosion risk may be caused by incorrect handling.  
• Do not throw batteries into a fire as they may explode.  
Replacement procedure  
• All memory contents will be cleared if you remove both batteries  
at the same time. Always replace each battery before removing  
the other one.  
• Make sure the power is turned off before replacing the batteries.  
• Do not press j until the battery replacement procedure is complete.  
1. Turn the power off by pressing @ o.  
2. Remove the two screws.  
3. Lift the battery cover to remove.  
116  
Appendix  
4. Remove one used battery by prying it out with a ball-point pen or similar  
pointed object.  
• Replace one battery at this step.  
5. Install a new battery with the positive side (+) facing up.  
6. Repeat steps 4 and 5 to replace the other battery.  
7. Replace the cover and screws.  
8. Press the RESET switch using the tip of a  
zALL DATA CL?z  
z YES¬[DEL] z  
z NO¬[ENTER]z  
ball-point pen or similar object.  
• If you cannot see the message on the  
right, repeat steps 1–7.  
9. Press e.  
• Do not press y. If y is pressed, the memory contents will be  
cleared.  
10. Adjust the LCD contrast. (See page 118.)  
Automatic power off function  
The calculator will turn itself off to save battery power if no key is pressed for  
approximately 10 minutes.  
117  
Appendix  
The OPTION menu  
The OPTION menu controls display contrast, memory checking and deletion  
of data.  
The OPTION display  
Press @ o (S key) to show the  
<OPTION>  
ƒCTRST ⁄M.CHK  
¤DELETE  
OPTION menu.  
• Press j to return to the mode in which  
you were working previously.  
Contrast  
Press 0 in the OPTION menu to show the  
LCD CONTRAST display.  
LCD CONTRAST  
[+] [-]  
DARK® ¬LIGHT  
• Press + to darken the display and  
- to lighten it.  
• It is possible to lighten the display so much  
that the calculator appears to be off. If the display remains blank when  
you press X, press @ o 0 and then press +  
repeatedly to darken the display.  
Memory check  
Press 1 in the OPTION menu to show the  
MEMORY CHECK display.  
624BYTES FREE  
EQTN: 15  
PROG: 09  
• The amount of free memory in bytes is  
shown on the first line. When the  
calculator is used for the first time, the  
following amount of memory is available.  
[EL-5250] 4,096 bytes  
[EL-5230] 1,280 bytes  
• The figures after EQTN are the numbers of equations (Filing equations  
functions) in the NORMAL mode.  
• The figures after PROG are the numbers of programs stored in the  
PROG mode.  
For a detailed description of how memory is used, refer to ‘Memory usage’.  
(See page 126.)  
118  
Appendix  
Deleting equation files and programs  
Press 2 in the OPTION menu to show the  
DELETE menu.  
<<DELETE>>  
ƒEQTN ⁄PROG  
• Press 0 or 1 to delete equation  
files or programs that have been stored  
in the NORMAL or PROG modes,  
respectively.  
After selecting the mode for which data is to be deleted, press y to  
delete data. Press e to cancel the operation.  
• Once a file has been deleted there is no way to recover it.  
To delete individual files, enter the mode that contains the data you want to  
delete and use the specific delete function from the menu. (See pages 59  
and 86.)  
If an Abnormal Condition Occurs  
Should an abnormal condition occur, such as none of the keys (including  
j) functioning, press the RESET switch located on the back of the  
calculator. Refer to page 32.  
119  
Appendix  
Error Messages  
The following table shows common error messages and suggestions for  
correcting the error.  
Error no.  
Error message  
Solution  
Verify you are using the correct syntax for  
the function you are trying to apply.  
01  
SYNTAX  
Check you have not attempted to divide by  
zero or made some other calculation error.  
02  
03  
CALCULATION  
NESTING  
Use of more than the available number of  
buffers was attempted. (There are 10  
buffers* for numeric values and 24 buffers  
for calculation instructions.)  
* 5 buffers in the CPLX mode.  
Make sure your program does not use the  
same label name to specify more than  
one location.  
04  
05  
LBL DUPLICATE  
LBL UNDEFINED  
Make sure your program does not have a  
Goto or Gosub command pointing to a  
label that does not exist. Note that you  
can include labels that are not pointed to  
by Goto or Gosub commands without  
affecting program operation.  
Make sure your program does not have  
more than 20 labels.  
06  
07  
LBL OVER  
Make sure your program does not have  
more than 10 levels of nested  
subroutines.  
GOSUB STACK  
Make sure your program does not have a  
Return command with no corresponding  
Gosub command.  
08  
09  
10  
CAN’T RETURN  
MEMORY OVER  
STORAGE FULL  
Not enough free memory remains for what  
you are trying to do. Delete unneeded  
files and try again.  
Make sure the maximum number of 99  
saved equations or 99 programs is not  
exceeded. Delete unneeded equations or  
programs and try again.  
Use of more than 100 data items in the  
STAT mode was attempted.  
The maximum number of 160 characters  
in the equation input buffer was  
exceeded.  
11  
DATA OVER  
You have pressed j to stop a  
(No number) BREAK!  
program or solver calculation.  
120  
Appendix  
Using the Solver Function Effectively  
The calculator uses Newton’s method to solve equations. (See page 52.)  
Because of this, the solution it provides may differ from the true solution, or  
an error message may be displayed for a soluble equation. This section  
shows how you can obtain a more acceptable solution or make the equation  
soluble in such cases.  
y = f(x)  
Newton’s method  
y
Tangential lines  
Newton’s method is a successive  
approximation technique that uses  
tangential lines. The calculator chooses  
an ‘approximate’ solution then calculates  
and compares the right-hand and left-  
Solution  
hand sides of the equation. Based on the  
result of this comparison, it chooses  
another ‘approximate’ solution. It repeats  
this process until there is hardly any  
discrepancy between the right-hand and  
left-hand sides of the equation.  
x
Initial value  
Newton’s method  
Intersections of dotted lines with  
the x-axis give successive  
approximate solutions found using  
Newton’s method.  
‘Dead end’ approximations  
When @ h is pressed for the first  
time, the calculator takes the value that is stored in memory, or zero if no  
value is stored, to be the initial expected value for the unknown variable and  
tries to solve the equation. If it fails to find an acceptable solution using this  
expected value, it tries again using up to nine more initial expected values  
until a solution is found. If none of the values  
lead by successive approximation toward an  
acceptable solution — but rather to a ‘dead  
end’ — the calculator will abort calculation and  
- ERROR 02 -  
CALCULATION  
display an error message.  
Range of expected values  
After the stored value (or zero) has been tried, new initial expected values  
are selected according to the range of expected values for the equation.  
(See ‘Changing the range of expected values’.) To choose which initial  
expected values to try, the calculator divides the range into eight subranges  
of equal width and tries each of the values at the edges of these subranges  
in turn (starting with the lower limit of the range of expected values, a).  
121  
Appendix  
Calculation accuracy  
• The calculator solves an equation by comparing the values of the left-  
hand and right-hand sides of the equation through 14-digit internal  
operations. If the value of the left-hand side is sufficiently close to  
agreeing with that of the right-hand side the calculator may present one  
of the ‘approximate’ values as a solution — even though it is not the true  
solution.  
• The calculator will also stop trying to solve an ‘approximate’ solution  
either when it has performed more than 50 iterations using each initial  
expected value or when it has obtained an ‘approximate’ solution that is  
the same (to 10-digit accuracy) twice in succession.  
Changing the range of expected values  
After entering your equation by pressing  
RANGE:a<b  
I 5, press @ J to adjust the  
range of expected values. The calculator will  
then prompt you for a range of expected  
values (between –1 × 1099 and +1 × 1099) to  
be used in the calculation.  
a=  
–1.  
1.  
b=  
a: Lower limit  
b: Upper limit  
• The range of expected values returns to its default setting (–1 × 1010 to  
+1 × 1010) when the current equation is cleared or the mode is changed.  
After entering the lower and upper limits (a and b) of the range of expected  
values, press j to return to the previous display.  
• The best solution can be found by defining the lower or upper limit (a or  
b) or initial value close to the expected solution.  
• Having done this, press @ h several times to generate slightly  
different solutions.You can judge which of these is the best by  
comparing the values displayed for the left-hand and right-hand sides of  
the equation.  
122  
Appendix  
y
Equations that are difficult to solve  
Newton’s method has problems in solving  
certain types of equations, either because  
the tangential lines it uses to approximate the  
solutions iterate only slowly toward the  
correct answer, or because they do not  
iterate there at all. Examples of such  
equations include equations of which steep  
slopes are a feature (e.g. y = 10x–5), periodic  
functions (e.g. y = sin x), functions featuring  
an inflection (e.g. y = x3–3x2 + x + 5) and  
functions where the unknown variable  
appears as a denominator (e.g. y = 8/x + 1).  
x
x
Solving y =10 – 5 for y = 0.  
Because of the steep slope, it  
takes a long time to iterate to the  
correct solution. Set limits a and  
b as close as possible either side  
of your expected solution.  
Many of those equations may become  
soluble if a range of expected values is  
defined that corresponds closely to the real  
solution.  
• For periodic functions such as sin x and  
cos x, the gradient near peaks or  
troughs is very shallow. If the initial  
expected value falls too close to a peak  
or trough, the calculator may iterate to  
a totally different cycle of the function  
and will not obtain an accurate solution.  
Make sure the initial expected value is  
an appropriate distance between a  
peak and a trough.  
Solving y = sin x for y = 0.  
If the Initial expected value is too  
close to a peak, the calculator  
will iterate away from the correct  
solution.  
y
• Where appropriate, you can try  
rearranging the equation so that the  
unknown variable is no longer a  
denominator.  
x
Solving y = x3 – 3x2 + x + 5 for  
y = 0.  
If the initial expected value is  
x = 3, no solution is obtained.  
However, setting x to –3 gives  
the correct solution of –1.  
123  
Appendix  
Technical Data  
Calculation ranges  
• Within the ranges specified, the calculator is accurate to 1 of the  
least significant digit of the mantissa. However, in continuous  
calculations the calculation error increases due to the  
accumulation of each successive calculation error. (This is the  
same for yx, x , n!, ex, In etc., where continuous calculations are  
performed internally.)  
• Furthermore, the calculation error will accumulate and become  
larger in the vicinity of inflection points and singular points of  
functions, and in programmed repetitive calculations.  
• Calculation ranges  
10-99 to 9.999999999 × 1099 and 0.  
If the absolute value of an entry or a final or intermediate result of a  
calculation is less than 10-99, the value is considered to be 0 in calculations  
and on the display.  
Function  
Dynamic range  
DEG: | x | < 1010  
(tan x : | x | 90 (2n–1))*  
=
/
π
RAD:  
| x | < —– × 1010  
sin x, cos x,  
tan x  
180  
π
2
(tan x : | x | — (2n–1))*  
=
/
10  
GRAD: | x | < —– × 1010  
9
(tan x : | x | 100 (2n–1))*  
=
/
sin–1x  
,
cos–1x  
| x | ≤ 1  
tan–1x, 3  
x
√
| x | < 10100  
10–99 ≤ x < 10100  
In x log x  
,
• y > 0: –10100 < x log y < 100  
• y = 0: 0 < x < 10100  
x
y
• y < 0: x = n  
1
x
=
/
(0 < l x l < 1: — = 2n–1, x 0)*,  
–10100 < x log | y | < 100  
1
x
• y > 0: –10100 < — log y < 100 (x = 0)  
/
• y = 0: 0 < x < 10100  
__  
x
y
• y < 0: x = 2n–1  
√
1
x
(0 < | x | < 1 : — = n, x = 0)*,  
–10100 < — log | y | < 100  
/
1
x
124  
Appendix  
Function  
Dynamic range  
–10100 < x ≤ 230.2585092  
–10100 < x < 100  
x
e
x
10  
sinh x, cosh x,  
tanh x  
sinh–1 x  
cosh–1 x  
tanh–1 x  
x2  
| x | ≤ 230.2585092  
| x | < 1050  
1 ≤ x < 1050  
| x | < 1  
| x | < 1050  
x3  
| x | < 2.15443469 × 1033  
__  
x
x–1  
0 ≤ x < 10100  
√
| x | < 10100 (x ≠ 0)  
0 ≤ n ≤ 69*  
n!  
0 ≤ r ≤ n ≤ 9999999999*  
nPr  
nCr  
n!  
—— < 10100  
(n-r)!  
0 ≤ r ≤ n ≤ 9999999999*  
0 ≤ r ≤ 69  
n!  
—— < 10100  
(n-r)!  
↔
DEG, D°M’S  
0°0’0.00001” ≤ | x | < 10000°  
x2 + y2 < 10100  
x, y → r,  
θ
0 ≤ r < 10100  
DEG: | θ | < 1010  
π
r, θ→ x, y  
RAD:  
| θ | < —– × 1010  
180  
10  
GRAD : | θ | < — × 1010  
9
DEG→RAD, GRAD→DEG: | x | < 10100  
DRG  
π
98  
—
RAD→GRAD: | x | <  
× 10  
2
(A+Bi)+(C+Di)  
| A + C | < 10100, | B + D | < 10100  
| A – C | < 10100, | B – D | < 10100  
(A+Bi)–(C+Di)  
(AC – BD) < 10100  
(AD + BC) < 10100  
×
(A+Bi) (C+Di)  
AC + BD  
< 10100  
C2 + D2  
(A+Bi)÷(C+Di)  
BC – AD  
< 10100  
C2 + D2  
C2 + D2 =  
/
0
125  
Appendix  
Function  
Dynamic range  
→DEC  
→BIN  
→PEN  
→OCT  
→HEX  
AND  
OR  
XOR  
XNOR  
DEC : | x | ≤ 9999999999  
BIN : 1000000000 ≤ x ≤ 1111111111  
0 ≤ x ≤ 111111111  
PEN : 2222222223 ≤ x ≤ 4444444444  
0 ≤ x ≤ 2222222222  
OCT : 4000000000 ≤ x ≤ 7777777777  
0 ≤ x ≤ 3777777777  
HEX : FDABF41C01 ≤ x ≤ FFFFFFFFFF  
0 ≤ x ≤ 2540BE3FF  
BIN : 1000000000 ≤ x ≤ 1111111111  
0 ≤ x ≤ 111111111  
PEN : 2222222223 ≤ x ≤ 4444444444  
0 ≤ x ≤ 2222222221  
OCT : 4000000000 ≤ x ≤ 7777777777  
0 ≤ x ≤ 3777777777  
HEX : FDABF41C01 ≤ x ≤ FFFFFFFFFF  
0 ≤ x ≤ 2540BE3FE  
BIN : 1000000001 ≤ x ≤ 1111111111  
0 ≤ x ≤ 111111111  
PEN : 2222222223 ≤ x ≤ 4444444444  
0 ≤ x ≤ 2222222222  
OCT : 4000000001 ≤ x ≤ 7777777777  
0 ≤ x ≤ 3777777777  
NOT  
NEG  
HEX : FDABF41C01 ≤ x ≤ FFFFFFFFFF  
0 ≤ x ≤ 2540BE3FF  
* n, r: integer  
Memory usage  
The amounts of memory the calculator uses for variables, programs and  
equations are shown below.  
Variables  
Each variable uses 1 byte, and each local variable uses 9 bytes to store  
its value.  
Programs  
Creating a new program uses 32 bytes of memory irrespective of the  
length of its name.  
Each line in a program uses 3 bytes plus the number of characters or  
commands on the line (each character or command uses 1 byte). For  
example, the two lines of the program shown below use 60 bytes.  
126  
Appendix  
Characters,  
For value  
Management commands and of local  
Total  
variables  
variables  
Program title  
If A=0 Goto ABC  
A¡=A+1  
32 bytes  
3 bytes  
3 bytes  
—
8 bytes  
5 bytes  
—
—
9 bytes  
32 bytes  
11 bytes  
17 bytes  
Total consumption  
38 bytes  
13 bytes  
9 bytes  
60 bytes  
Filing Equation functions  
Each stored equation uses 30 bytes plus the number of characters or  
commands.  
Priority levels in calculations  
Operations are performed according to the following priority:  
ቢ Fractions (1ı4, etc.)  
ꢀ ∠ , engineering prefixes  
ቤ Functions preceded by their argument (x−1, x2, n!, etc.)  
ꢁ Yx, x  
ቦ Implied multiplication of a memory value (2Y, etc.)  
ቧ Functions followed by their argument (sin, cos, (–), etc.)  
ቨ Implied multiplication of a function (2sin30, etc.)  
ቩ nCr, nPr  
ቪ ×, ÷  
ꢂ +, −  
ቭ AND  
ቮ OR, XOR, XNOR  
ቯ =, M+, M−, ⇒M, ̈DEG, ̈RAD, ̈GRAD, DATA, CD, →rθ, →xy,  
and other calculation ending instructions  
• If parentheses are used, the parenthesized calculations have precedence  
over the other calculations.  
127  
Appendix  
Specifications  
Model:  
EL-5230/5250  
Display type:  
[14 characters and 2 exponents] × 3 rows  
5 × 7 dots /character  
Dot matrix characters:  
Number of display digits:  
Input ranges:  
10-digit mantissa + 2-digit exponent  
10-99 to 9.999999999 × 1099 and 0.  
(up to 10-digit mantissa)  
Number of internal  
calculation digits:  
14-digit mantissa  
Pending operations:  
24 calculations 10 numeric values (5 numeric  
values in the CPLX modes)  
Calculation functions:  
Calculations (four basic arithmetic  
operations, calculations with parentheses,  
memory calculations, function calculations,  
etc.), differential/integral functions, binary/  
pental/octal/decimal/hexadecimal operations,  
solver functions, simulation calculations,  
complex number calculations, etc.  
Statistical calculations:  
Equation solvers:  
Programming function:  
Option menu:  
One-variable statistics, two-variable statistics,  
normal probability calculations, etc.  
Simultaneous linear equations, and  
quadratic/cubic equation solvers.  
New programming, running a program, and  
editing a program and deleting a program.  
LCD contrast, memory check and data  
deletion  
Memory capacity:  
[EL-5250] 4,096 bytes (user area)  
[EL-5230] 1,280 bytes (user area)  
Power source:  
3 V (DC):  
Lithium battery (CR 2032) × 2  
Auto power off:  
After approximately 10 minutes  
0.002 W  
Power consumption:  
Operating temperature:  
Operating time:  
0°C – 40°C (32°F – 104°F)  
Approximately 1,800 hours* (at 25°C (77°F),  
assuming each hour consists of 5 minutes of  
continuous operation and 55 minutes of  
display time).  
128  
Appendix  
Dimensions:  
Weight:  
79.6 mm (W) × 154.5 mm (D) × 15.2 mm (H)  
3-1/8” (W) × 6-3/32” (D) × 19/32” (H)  
Approx. 97 g (0.22 lb) (including batteries,  
but not including hard case)  
Accessories:  
2 lithium batteries (installed), operation  
manual, quick reference card and hard case  
* This value may vary according to the way the calculator is used and other  
factors.  
For More Information about Scientific Calculators  
Visit our Web site.  
http://sharp-world.com/calculator/  
In Europe:  
This equipment complies with the requirements of Directive 89/336/EEC as amended by 93/  
68/EEC.  
Dieses Gerät entspricht den Anforderungen der EG-Richtlinie 89/336/EWG mit Änderung 93/  
68/EWG.  
Ce matériel répond aux exigences contenues dans la directive 89/336/CEE modifiée par la  
directive 93/68/CEE.  
Dit apparaat voldoet aan de eisen van de richtlijn 89/336/EEG, gewijzigd door 93/68/EEG.  
Dette udstyr overholder kravene i direktiv nr. 89/336/EEC med tillæg nr. 93/68/EEC.  
Quest’ apparecchio è conforme ai requisiti della direttiva 89/336/EEC come emendata dalla  
direttiva 93/68/EEC.  
ꢀ ꢁꢂꢃꢄꢅꢆꢇꢅꢄꢇꢈ ꢄꢉꢅꢊ ꢄꢋꢅꢄꢌꢍꢃꢎꢏꢋꢁꢅꢄꢐ ꢇꢅꢐꢑ ꢄꢌꢄꢐꢅꢊꢇꢁꢐꢑ ꢅꢒꢋ ꢍꢓꢈꢂꢐꢔꢋ ꢅꢈꢑ ꢕꢉꢎꢒꢌꢄꢖꢃꢊꢑ  
ꢕꢋꢒꢇꢈꢑ 89/336/ꢕꢗꢘ, ꢙꢌꢒꢑ ꢍ ꢃꢄꢋꢍꢋꢐꢇꢚꢙꢑ ꢄꢉꢅꢙꢑ ꢇꢉꢚꢌꢛꢈꢎꢔꢜꢈꢃꢁ ꢄꢌꢙ ꢅꢈꢋ ꢍꢓꢈꢂꢏꢄ 93/68/  
ꢕꢗꢘ.  
Este equipamento obedece às exigências da directiva 89/336/CEE na sua versão corrigida pela  
directiva 93/68/CEE.  
Este aparato satisface las exigencias de la Directiva 89/336/CEE modificada por medio de la  
93/68/CEE.  
Denna utrustning uppfyller kraven enligt riktlinjen 89/336/EEC så som kompletteras av 93/68/  
EEC.  
Dette produktet oppfyller betingelsene i direktivet 89/336/EEC i endringen 93/68/EEC.  
Tämä laite täyttää direktiivin 89/336/EEC vaatimukset, jota on muutettu direktiivillä 93/68/  
EEC.  
чÌÌÓ ÛÒÚÓÈÒÚ‚Ó ÒÓÓÚ‚ÂÚÒÚ‚ÛÂÚ Ú·ӂ‡ÌËflÏ ‰ËÂÍÚË‚˚ 89/336/EEC Ò Û˜ÂÚÓÏ  
ÔÓÔ‡‚ÓÍ 93/68/EEC.  
Ez a készülék megfelel a 89/336/EGK sz. EK-irányelvben és annak 93/68/EGK sz.  
módosításában foglalt követelményeknek.  
Tento pfiístroj vyhovuje poÏadavkÛm smûrnice 89/336/EEC v platném znûní 93/68/EEC.  
129  
SHARP CORPORATION  
04LGK (TINSE0796EHZZ)  
PRINTED IN CHINA / IMPRIMÉ EN CHINE / IMPRESO EN CHINA  

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