HP (Hewlett Packard) HP 6S User Manual

HP 6S Scientific Calculator  
H
1
Contents  
1. Keyboard  
5
General keys  
5
5
5
5
6
6
Memory keys  
Special keys  
Base-n keys  
Function keys  
Statistical keys  
2. The display  
7
Exponent displays  
7
3. Basic functions  
8
Entering numbers  
Entering negative numbers  
Entering exponential numbers  
Arithmetic operator  
Equals  
Making corrections  
Clearing errors  
Fixing the number of decimal places displayed  
Setting the display to scientific notation  
8
8
8
8
8
9
9
9
9
4. Calculations  
10  
Precision  
Order of operations  
Simple calculations  
Specifying the order of calculations  
Re-using arithmetic operations  
Using memory  
10  
10  
10  
10  
11  
11  
11  
12  
Fraction arithmetic  
Percentage calculations  
5. Other functions  
13  
Converting minutes and seconds to decimal format  
Conversion between angles, radians and grads  
Trigonometric functions  
Hyperbolic functions  
Logarithmic functions  
Powers and roots  
Miscellaneous functions  
Polar to rectangular coordinates conversions  
Rectangular to polar coordinates conversions  
13  
13  
13  
14  
14  
14  
15  
15  
15  
3
6. Binary, octal and hexadecimal values  
Binary/octal/decimal/hexadecimal conversions  
Binary/octal/decimal/hexadecimal calculations  
Logical operations  
16  
16  
16  
17  
18  
Radix complement  
7 . Using statistics  
19  
19  
19  
Entering a list of data items to analyse  
Using statistical functions on your data  
8 . Specifications  
20  
21  
9 . Changing the battery  
4
1. Keyboard  
General keys  
Key  
Functions  
Page  
Key  
Functions  
Page  
0 to9:. Data entry  
8
ØÅ  
Sexagesimal/decimal  
notation conversion  
13  
+-*  
d=  
Basic calculation  
8
¯
Ù
Mode of angle  
DEGRADGRADDEG  
13  
13  
¡
Reset the calculator  
and clear the memory  
9
Angular conversion of data  
DEGRADGRADDEG  
Ô
Ó
Clear/clear error  
Change sign  
9
8
²
Õ
Register exchange  
11  
9
Clearing the last  
entered digit  
Memory keys  
¼
Fix the number of digits  
after the decimal point  
9
Key  
Functions  
Page  
»
½
¾
Floating notation  
9
9
r
Retrieve data from the  
independent memory  
11  
Scientific notation  
Engineering notation  
´
³
m
Store display data in  
memory  
11  
11  
11  
15  
Base-n keys  
Exchange of display data  
and contents of memory  
Key  
Functions  
Page  
Add displayed data to  
memory  
¤
Decimal  
16  
¥
Binary  
16  
16  
16  
Special keys  
¦
Hexadecimal  
Octal  
Key  
Functions  
Page  
§
I
Inverse  
7
A to F  
Hexadecimal numbers only 16–18  
M
()  
¹
P
Mode  
7
10  
8
&
o
And  
17  
17  
17  
17  
17  
18  
Brackets (parentheses)  
Or  
Exponent  
Pi  
x
X
Ì
N
Exclusive Or  
Exclusive Nor  
Not  
13  
Negative  
Keyboard  
5
Function keys  
K e y  
Functions  
Page  
K e y  
Functions  
Page  
s
Sine  
13  
É
Power  
8
c
t
S
¨
T
ª
L
Û
È
Cosine  
13  
13  
13  
13  
13  
14  
14  
14  
14  
14  
14  
14  
12  
14  
12  
14  
Ê
Ä
Ã
%
Root  
14  
15  
15  
12  
Rectangle to polar  
Polar to rectangular  
Percent  
Tangent  
Arc sine  
Arc cosine  
Arc tangent  
Hyperbolic  
Common logarithm  
Common antilogarithm  
Natural logarithm  
Natural antilogarithm  
Square root  
Square  
Statistical keys  
Key  
Functions  
Page  
¿
Statistical data mode  
Data entry  
19  
À
Á
Ñ
Ò
Ï
19  
19  
19  
Ð
Data delete  
Â
º
Sample standard deviation  
Population standard deviation 19  
ˬ  
Ý
Ç
Fraction  
Arithmetic mean  
Number of data  
Sum of value  
19  
19  
19  
19  
Cube root  
n
Reciprocal  
Factorial  
Í
Î
Æ
Sum of square value  
Keyboard  
6
2. The display  
M
E
1
2 3 4 5  
.
INV HYP BIN OCT HEX  
Mantissa  
LCD Diagram  
The display shows input data, interim results and answers to calculations. The mantissa section displays up to 10  
digits. The exponent section displays up to ±99.  
Display  
Meaning  
Page  
-E-  
Indicates an error  
9
INV  
I has been pressed to enable inverse key functions  
Indicates that data is stored in the memory  
ª has been pressed for hyperbolic functions  
BASE-N mode has been selected  
9
M
HYP  
11  
14  
16  
19  
13  
BIN, OCT, HEX  
SD  
Statistical mode has been selected  
DEG, RAD, GRAD  
¯ has been pressed to switch between the DEG, RAD and GRAD  
angle types  
FIX (this does not display) The number of decimal places of a displayed value has been set  
9,15  
9
SCI (this does not display) Converts a displayed value to exponent display  
ENG (this does not display) Converts a displayed value to exponent display of which the exponent  
15  
is a multiple of 3 and mantissa is between 0 to 999  
FLO (this does not display) Convert a SCI or ENG form display to a normal display value  
15  
11  
13  
45Ö12×123  
4512/123  
12.°3'45.6"  
Sexagesimal figure 12°3'45.6"  
Exponent displays  
The display can show calculation results only up to 10 digits long. When an intermediate value or a final result is  
longer than 10 digits, the calculator automatically switches over to exponential notation. Values greater than  
9,999,999,999 are always displayed exponentially.  
The Display  
7
3. Basic functions  
Entering numbers  
123  
Press the number keys to enter numbers.  
Press . for a decimal point.  
etc  
.
Entering negative numbers  
Ó
Press after a number to make it negative.  
5.08Ó  
-5.08  
Entering exponential numbers  
¹
Press to enter an exponential number.  
3.08×109  
3.08¹9  
3.0809  
Arithmetic operator  
Press to perform an arithmetic operation on the value displayed.  
You must enter a number after the arithmetic operator.  
If you press more than one arithmetic operator in sequence, the calculator only performs  
the last operation (the last key pressed).  
+-*  
dÉ  
4*d+-+5  
9.  
Equals  
=
Press to complete your calculation and display a result. If you press = more than once  
without entering a number, the calculator performs the last arithmetic operation on the value  
displayed.  
4×8  
4*8=  
32.  
4*8==  
256.  
Basic functions  
8
Making corrections  
Õ
Press to delete the last number entered.  
Ô
Press to remove the displayed value, but retain the calculation being performed.  
Press after the arithmetic operator to cancel the entire calculation.  
5+5+5+6Ô5=  
5+5+5+Ô=  
20.  
0.  
Clearing errors  
Ô
¡
Press to clear an error (indicated by “-E-“ in the display)—eg, an overflow error—and retain  
data in the memory.  
Press to reset the calculator and clear the memory (solar model only).  
Fixing the number of decimal places displayed  
I¼  
2
Press after your arithmetic operation, or after you press ¡, to set the number of decimal  
places displayed (the number you press is the number of decimal places you want to  
display). The calculator rounds the number in the display but maintains full precision internally.  
I
Press to reset the floating decimal point.  
¼.  
Setting the display to scientific notation  
I
½
Press to set the display to scientific notation and express the number as a power of 10—eg,  
.0043 is displayed as 4.3.-03 to represent 4.3×10-3.  
I
»
Press to reset the display to the floating format.  
Basic functions  
9
4. Calculations  
Precision  
The HP 6S scientific calculator calculates answers to 12-digit accuracy, but rounds answers  
to 10 digits in the display. When it performs a calculation using the result of a previous  
calculation, it uses the stored 12-digit value and not the 10-digit value displayed.  
Order of operations  
The HP 6S scientific calculator performs operations in the following order:  
º, Ê, Ä, Ã  
*, d  
+, -  
&
o, x, X  
Simple calculations  
Perform calculations in the same way that you write them on paper.  
7.2×8.5 – 4.7×3.9  
7.2*8.5-4.7*3.9=  
42.87  
32.  
4×8  
4*8=  
Specifying the order of calculations  
( )  
Use brackets to specify the order of calculations. You can nest as many as six levels of  
brackets.  
You do not need to enter the closing brackets. The calculator inserts them for you, although it  
does not display them.  
-5(4+3)  
5Ó*(4+3=  
-35.  
Calculations  
10  
Re-using arithmetic operations  
Press the arithmetic operator key twice to re-use an arithmetic operation on a new number. The  
++  
or  
calculator stores the operation and applies it when you enter another number and press =.  
Store a calculation for re-use by enclosing it in brackets.  
**  
etc  
Clear the stored arithmetic operation by pressing Ô.  
3+2.3  
6+2.3  
9+2.3  
4(3×6)  
-5(3×6)  
3++2.3=  
6=  
5.3  
8.3  
9=  
11.3  
72.  
4**(3*6=  
5Ó=  
-90.  
Using memory  
´
m
The HP 6S scientific calculator has one independent memory.  
M is displayed when there is a value in memory.  
r
³
Ô
¡
Press Ô to clear the display or cancel the current calculation without clearing the memory.  
Press ´ to store the displayed value in memory.  
Press m to add the displayed value to the memory.  
Press r to retrieve the contents of memory—to determine its value or include it in your  
calculation.  
f
e
Press to display the contents of memory and replace it with the value that was  
displayed before the keys were pressed.  
Press ¡ to clear the display and the memory (solar model).  
Press fe to clear the display and the memory (battery model).  
Fraction arithmetic  
Ë
Press to enter fractions.  
Press Ë after = to display the fraction as a decimal.  
In the display, a fraction is reduced to its lowest terms when you press a function command  
key (×,÷,+,-) or =.  
4 5/6 × (3+12/3) ÷ 78/9  
4Ë5Ë6*(3+1Ë2Ë3)d7Ë8Ë9=  
Ë
2Ö61×71.  
2.86  
Calculations  
11  
(1.5×107) – [(2.5×106) × 3/100] =  
1.5¹7-2.5¹6*3Ë100= 149250000.  
3456/78 = 811/13  
3Ë456Ë78  
=
3Ö456×78.  
8Ö11×13.  
I¬  
Press these keys to switch between proper and improper fractions.  
811/13 = 115/13  
8Ö11×13.  
115×13.  
8Ö11×13.  
I¬  
I¬  
The answer to a calculation involving both fractions and decimals is displayed as a decimal.  
41/52 × 78.9  
41Ë52*78.9= 62.20961538  
Percentage calculations  
I%  
Press to perform percentage calculations.  
12% of 1500  
1500*12I%=  
660d880I%=  
2500+15I%  
=
180.  
75.  
660 as a percentage of 880  
2500 plus 15%  
375.  
2875.  
875.  
2625.  
25% discount on 3500  
3500-25I%  
=
26% of 2200; 26% of 3300; 26% of 3800;  
2200**26I%=  
572.  
858.  
988.  
3300=  
3800=  
$80 last week; $100 this week: what % is the new value of the old value?  
100d80I%=  
125.  
What % is 138gm to 150gm and 129gm to 150gm?  
138dd150I%=  
129=  
92.  
86.  
Calculations  
12  
5. Other functions  
Converting minutes and seconds to decimal format  
Ø
Press to convert minutes and seconds (sexagesimal figure) to decimal format. When you  
enter the sexagesimal figure, enter the degrees to the left of the decimal point, and minutes  
and seconds to the right—the first and second digits to the left of decimal point are minutes  
and the third and subsequent digits seconds.  
IÅ  
Press to convert decimal format to sexagesimal format.  
14°2536″  
14.2536Ø  
14.42666667  
IÅ  
14°2536″  
Conversion between angles, radians and grads  
IÙ  
45° = 0.785398163 rad = 50 grad  
45IÙ RAD 0.785398163  
GRAD  
50.  
45.  
DEG  
Trigonometric functions  
Press ¯  
sin (π/6 rad) =  
to switch  
RAD IPd6=s RAD  
0.5  
between  
RAD, DEG  
and GRAD  
cos 63°5241=  
DEG 63.5241Ø DEG 63.87805556  
DEG 0.440283084  
c
tan (-35 grad) =  
GRAD 35Ót GRAD-0.612800788  
2 sin 45° x cos 65° = DEG 2*45s*65c= DEG 0.597672477  
cot 30° = 1/tan 30° =  
DEG 30tÇ DEG 1.732050808  
1
sec (π/3 rad) = cos (π/3 rad)  
RAD IPd3=cÇ RAD  
30sÇ DEG  
2.  
2.  
1
cosec 30° = sin 30°  
-
2  
cos  
2
RAD 2IÂÓd2=c RAD 0.760244597  
tan –10.6104 =  
DEG .6104IT DEG 31.39989118  
DEG  
IÅ  
31°2359.6″  
Other functions  
13  
Hyperbolic functions  
sinh 3.6 =  
3.6ªs  
2.5ªt  
18.28545536  
0.986614298  
tanh 2.5 =  
M
M
cosh 1.5 – sinh 1.5 =  
1.5´ªc-  
rªs=  
2.352409615  
0.22313016  
sinh –1 30 =  
30IªS  
4.094622224  
0.343941914  
solve tanh 4x = 0.88  
tan 10.88  
x =  
=
.88IªTd4=  
4
Logarithmic functions  
log 1.23 (=log10 1.23) =  
1.23L  
0.089905111  
solve 4x = 64 log 64  
x = log4  
64Ld4L=  
456´LdrÈ=  
.4IÛ+5*3ÓIÐ=  
5.6É2.3=  
3.  
0.434294481  
2.760821773  
52.58143837  
1.988647795  
1.305111829-21  
553467.4658  
M
log 456 ÷ In 456 =  
100.4 + 5 e .3  
5.62.3  
1231/7 (=7123) =  
(78 – 23)-12  
=
=
123IÊ7=  
=
(78-23)É12Ó=  
3É12+10IÐ=  
312 + e10  
=
Powers and roots  
2 + 3 x 5 =  
35 + 3-27 =  
123 + 302 =  
2IÂ+3IÂ*5IÂ=  
5IÝ+27ÓIÝ  
123+30º=  
5.287196909  
-1.290024053  
1023.  
8! (=1 x 2 x 3 x ꢀ x 7 x 8 ) =  
8IÆ  
40320  
Otherfunctions  
14  
Miscellaneous functions  
1.234 + 1.234 =  
I¼21.234+  
1.234=  
1.23  
2.47  
I¼.  
2.468  
1 ÷ 3 + 1 ÷ 3 =  
I¼21d3+  
I½  
0.33  
3.33-01  
6.67-01  
0.67  
1d3=  
I»  
I¼. 0.666666666  
123m x 456m = 56088m  
= 56.088km  
123*456=  
56088.  
I¾  
56.088 03  
7.8g ÷ 96 = 0.08125g  
= 81.25mg  
7.8d96=  
I¾  
0.08125  
81.25 - 03  
Polar to rectangular coordinates conversions  
Formula: x = r cosθ  
y = r sinθ  
eg, find the value of x and y when the point P is shown  
as θ=60 and the length r=2 in the polar coordinates  
DEG 2I²60IÃ  
1.  
(x)  
1.732050808  
(y)  
I²  
1.  
(x)  
Rectangular to polar coordinates conversions  
Formula: r = x2 + y2  
y
θ = tan-1 / (-180°<θ ≥ 180°)  
x
eg, find the length r and the angle θ in radian when the point  
P is shown as x=1 and y=3 in the rectangular coordinates.  
RAD 1I²3IÂÄ=  
2.  
(r)  
1.047197551  
(θ in radian)  
I²  
2.  
(r)  
Otherfunctions  
15  
6. Binary, octal and hexadecimal values  
Use the M key to set the number base. When you use bases other than 10, you can only  
M
enter numbers valid for the base—eg, in binary mode you can only enter 1 and 0.  
¦§  
¥¤  
sets the mode to hexadecimal. In hexadecimal mode, A to F keys are enabled.  
Note that b and d in hexadecimal mode are shown in lower case to distinguish them from  
numbers.  
sets the mode to octal.  
sets the mode to binary.  
sets the mode to decimal.  
Note: When using a number base other than 10, any fractional part is truncated.  
Binary/octal/decimal/hexadecimal conversions  
Conversion of 2210 to binary.  
Conversion of 2210 to octal.  
Conversion of 51310 to binary.  
22M¥  
BIN  
10110.  
26.  
M§  
OCT  
E BIN  
513M¥  
0.  
Conversion to binary mode generates an error if the result is greater than 10 digits.  
Conversion of 7FFFFFFF16 to decimal.  
M¦7FFFFFFFM¤  
2147483647.  
Conversion of 12345610 to octal.  
123456M§  
OCT  
361100.  
102.  
Conversion of 11001102 to decimal.  
M¥1100110M¤  
Binary/octal/decimal/hexadecimal calculations  
M
101112 + 110102 = 1100012  
¦§  
¥¤  
M¥1011+1101=  
BIN  
11000.  
1238 x ABC16  
=37AF416  
M§123*M¦ABC=  
M¤  
HEX  
37AF4.  
=22808410  
228084.  
1F2D16 – 10010  
=788110  
M¦1F2D-M¤100  
M¦=  
7881.  
=1EC916  
HEX  
1EC9.  
Binary, octal and hexadecimal values  
16  
76548 ÷ 1210  
= 334.33ꢀ.10  
= 5168  
M§7654dM¤12=  
334.3333333  
M§  
OCT  
516.  
Fractional parts of calculation results are truncated.  
1102+4568x7810÷1A16  
=39016  
M¥110+M§456*  
M¤78dM¦1A=  
M¤  
HEX  
390.  
912.  
=91210  
Multiplication and division are given priority over addition and subtraction in mixed calculations.  
BC16 x (1410 + 6910  
=1560410  
=3CF416  
M¦BC*(M¤14+69)=  
M¦  
15604.  
3CF4.  
HEX  
Logical operations  
You can use the following logical operations to compare two numbers. When performing  
logical operations, keep the following points in mind:  
&o  
xX  
Ì
You cannot use decimal-base numbers in logical operations.  
The calculator compares the binary versions of the numbers you enter. If the number is  
less than 10 digits long, the calculator fills values to the left of the number with 0s—eg, if  
you compare hexadecimal F1 to octal 4, the calculator compares 0000010001 to  
0000000100.  
If you use one number with a logical operation, the calculator compares it to 0000000000.  
The logical operators work in the following way:  
1. The operation compares the binary digits in the corresponding positions in each of the  
numbers.  
2. The operation returns a binary digit corresponding to each position.  
3. If you are using a base other than binary, the result is shown in the base of the last  
number you entered.  
The following logical operators are available:  
& returns a 1 for every position where there is a 1 in both numbers.  
o returns a 1 for every position where there is a 1 in either number.  
x returns a 1 for every position where there is a 1 in either number, but not both numbers.  
X returns a 1 for every position where there is the same digit in both numbers.  
Ì returns the diminished radix complement.  
Press these keys to perform the respective binary, octal, decimal and hexadecimal logical  
operations.  
Binary, octal and hexadecimal values  
17  
1916AND 1A16 = 1816  
M¦19&1A=  
HEX  
18.  
12016OR 11012 = 12D16  
M¦120oM¥1101=  
M¦  
BIN  
100101101.  
HEX  
12d.  
516XOR 316 = 616  
M¦5X3=  
HEX  
6.  
2A16XNOR 5D16 = FFFFFFFF8816  
M¦2AX5D= HEX FFFFFFFF88.  
1A16 AND 2F16 =A16  
M¦1A&&2F=  
HEX  
BIN  
A.  
NOT of 10102  
M¥10110Ì  
1111101001.  
Radix complement  
IN  
Press to calculate and display the radix complement of the hexadecimal, octal or binary  
number currently displayed—ie, 10000000000-the binary version of the number.  
Binary, octal and hexadecimal values  
18  
7. Using statistics  
M¿  
Press to use statistics mode. Statistics mode allows you to enter data and apply the statistics  
functions to analyse the data.  
Entering a list of data items to analyse  
À
Press after each data element. When you press À, the calculator displays the number of  
data elements entered.  
For example, to enter a list of data consisting of 5, 8 and -3, use the following keystrokes:  
5 À 8 À3 Ó À  
To enter the results of a calculation as a data item, perform the calculation as you would  
normally, then press À when the answer is displayed.  
You can amend the data entered into the calculator:  
To cancel the last entry you made, press Ô before you press À. Note that when you  
press Ô, 0 is displayed. Press In to display the number of data elements stored in the  
calculator. To delete a data item you entered previously, enter the value again, then press  
.  
Using statistical functions on your data  
Once you enter a list of data values you can use the following statistical functions:  
In The number of data elements entered  
Sample standard deviation  
In  
ÒÑ  
ÏÍ  
Î
IÑ  
IÏ  
Population standard deviation  
Arithmetic mean  
IÍ  
IÎ  
The sum of each data element  
The sum of the data elements squared  
À
Find the sample standard deviation of the data 5, 9 13 and 6.  
M¿5À9À13À6ÀIÒ  
SD  
3.593976442  
4, 1, 82, 59, 2, and 103 were entered, but 59 was entered by  
mistake. It should have been 58. To fix the mistake, enter the  
wrong number, 59, and , then enter the right number,  
58, and À.  
Using statistics  
19  
8. Specifications  
Scientific functions/input range  
sinx / cosx / tanx  
|x|<4.5x1010 degrees  
(<25x107πrad,<5x1010grad  
|x|1  
|x|<10100  
sin-1x / cos-1x  
tan-1x  
sinhx / coshx  
|x|230.2585092  
|x|<10100  
tanhx  
sinh-1x  
cosh-1x  
tanh-1x  
logx / Inx  
ex  
|x|<5x1099  
|x|x<5x1099  
|x|<1  
10-99x<10100  
-10100<x230.2585092  
-10100<x<100  
10x  
yx  
y>010100<xlogy<100  
y=0x>0  
y<0x : integer or 1/2n +1 (n : integer)  
y>0x0 : -10100< 1/xlogy<230.2582092  
y=0x>0  
xy  
y<0x : odd number or 1/n (n : integer)  
0x<10100  
x  
x2  
|x|<1050  
3x  
1/x  
|x|<10100  
|x|<10100(xo)  
n!  
0x<69 (x: integer)  
x2 + y2<10100  
|θ|<4.5x1010 degrees  
(<25x107rad, <5x1010grad)  
0r10100  
RECPOL  
POLREC  
DMSDEG  
DEGDMS  
π
|x|10100  
|x|107  
10 digits  
Binary  
Positive:  
Negative: 1000000000x1111111111  
Positive: 0x3777777777  
Negative: 4000000000x7777777777  
Positive: 0x9999999999  
Negative: -9999999999x<0  
Positive: 0x2540BE3FF  
Negative: FDABF41C01xFFFFFFFFFF  
0x1111111111  
Octal  
Decimal  
Hexadecimal  
Specifications  
20  
Read-out  
Liquid crystal display suppressing unnecessary 0s (zeros).  
Power source  
Silicon solar cell (solar model only)  
Alkaline manganese battery (LR43)—1 battery for the solar model; 2 batteries for the non-solar model.  
Ambient Temperature range  
0°C–40°C (32°F–104°F).  
Dimensions  
127mmH x 72mmW x 8.5mmD (not including the wallet).  
Net weight  
91g (including wallet).  
9. Changing the battery  
·
Replace the battery when:  
Replace the battery (alkaline manganese battery (LR43)—1 in the solar model and 2 in the non-solar model)  
when the display darkens under poor light condition, or disappears, and cannot be restored by pressing ¡.  
·
To replace the battery:  
1.  
2.  
3.  
4.  
5.  
6.  
Remove the four screws at the back of the calculator. Don’t loose the screws.  
Remove the back panel.  
Remove the old battery. Lever it out with a sharp object like a pen.  
Install the new battery with the + sign at the uppermost.  
Replace the back panel and the screws.  
Check the display to make sure it is showing 0 in DEG mode.  
Changing the battery  
21  

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