HP 6S Scientific Calculator

English.PM6

3/3/99, 3:45 PM
NOTICE This manual and any examples contained herein are provided as is and are subject to change without notice. Except to the extent prohibited by law, Hewlett-Packard Company makes no express or implied warranty of any kind with regard to this manual and specifically disclaims the implied warranties and conditions of merchantability and fitness for a particular purpose and Hewlett-Packard Company shall not be liable for any errors or for incidental or consequential damage in connection with the furnishing, performance or use of this manual and the examples herein. Hewlett-Packard Company 1999. All rights reserved.
REGULATORY INFORMATION USA This calculator has been tested and found to comply with the limits for a Class B digital device, pursuant to part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This calculator generates, uses and can radiate radio frequency energy and may interfere with radio and television reception. In the unlikely event that this equipment does cause interference to radio or television reception, try the following: reorient or relocate the receiving antenna increase separation between the calculator and the receiver consult your dealer or an experienced radio/TV technician for help.
CANADA This Class B digital apparatus complies with Canadian ICES-003. Cet appareil numrique de la classe B est conforme la norme NMB-003.

Contents

1. Keyboard
General keys Memory keys Special keys Base-n keys Function keys Statistical keys

2. The display

Exponent displays

3. Basic functions

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

4. Calculations

Precision Order of operations Simple calculations Specifying the order of calculations Re-using arithmetic operations Using memory Fraction arithmetic Percentage calculations

5. Other functions

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
6. Binary, octal and hexadecimal values
Binary/octal/decimal/hexadecimal conversions Binary/octal/decimal/hexadecimal calculations Logical operations Radix complement

7. Using statistics

Entering a list of data items to analyse Using statistical functions on your data
8. Specifications 9. Changing the battery

General keys

Key Functions
Data entry Basic calculation

Page 8

Functions
Sexagesimal/decimal notation conversion Mode of angle

DEGRADGRADDEG

Page 15

0 to9:. +-* d=

Reset the calculator and clear the memory Clear/clear error Change sign
Angular conversion of data
Register exchange Clearing the last entered digit Fix the number of digits after the decimal point Floating notation Scientific notation Engineering notation

Memory keys

Retrieve data from the independent memory Store display data in memory Exchange of display data and contents of memory Add displayed data to memory

Page 11 11

Base-n keys

Key Functions

Decimal Binary Hexadecimal Octal Hexadecimal numbers only And Or Exclusive Or Exclusive Nor Not Negative

Page 18

Special keys
Inverse Mode Brackets (parentheses) Exponent Pi

Page 13

I M () P

A to F & o x X N

Keyboard

Function keys

Key s c t S T L Functions
Sine Cosine Tangent Arc sine Arc cosine Arc tangent Hyperbolic Common logarithm Common antilogarithm Natural logarithm Natural antilogarithm Square root Square Fraction Cube root Reciprocal Factorial

Page 14

Key %
Power Root Rectangle to polar Polar to rectangular Percent

Page 12

Statistical keys

Key n Functions

Statistical data mode Data entry Data delete Sample standard deviation Population standard deviation Arithmetic mean Number of data Sum of value Sum of square value

Page 19

1. 4 5

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 -EINV M HYP BIN, OCT, HEX SD DEG, RAD, GRAD FIX (this does not display) Meaning Indicates an error I has been pressed to enable inverse key functions Indicates that data is stored in the memory has been pressed for hyperbolic functions BASE-N mode has been selected Statistical mode has been selected has been pressed to switch between the DEG, RAD and GRAD angle types The number of decimal places of a displayed value has been set Page 13 9,11 13
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 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 4512123 12.3'45.6" 4512/123 Sexagesimal figure 123'45.6"
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

Entering numbers
etc Press the number keys to enter numbers. Press. for a decimal point.
Entering negative numbers
Press after a number to make it negative. 5.08 -5.08
Entering exponential numbers
Press to enter an exponential number. 3.08109 3.089 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). 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. 48 4*8= 4*8== 32. 256.

Basic functions

Making corrections
Press to delete the last number entered. 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+65= 5+5+5+= 20. 0.

Clearing errors

Press to clear an error (indicated by -E- in the display)eg, an overflow errorand retain data in the memory. Press to reset the calculator and clear the memory (solar model only).
Fixing the number of decimal places displayed

I 2 I.

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. Press to reset the floating decimal point.
Setting the display to scientific notation
Press to set the display to scientific notation and express the number as a power of10eg,.0043 is displayed as 4.3.-03 to represent 4.310-3. Press to reset the display to the floating format.

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: , , , *, d +, & o, x, X

Simple calculations

Perform calculations in the same way that you write them on paper. 7.28.5 4.73.9 7.2*8.5-4.7*3.9= 48 4*8= 42.87 32.
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) 5*(4+3= -35.

Calculations

Re-using arithmetic operations
or Press the arithmetic operator key twice to re-use an arithmetic operation on a new number. The 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. Clear the stored arithmetic operation by pressing. 3+2.3 6+2.3 9+2.3 4(36) -5(36) 3++2.3= 6= 9= 4**(3*6= 5= 5.3 8.3 11.3 72. -90.

Using memory

f e The HP 6S scientific calculator has one independent memory. M is displayed when there is a value in memory. Press 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 memoryto determine its value or include it in your calculation. Press I 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

Press to enter fractions. Press 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) 78/9 456*(3+123)d789= 26171. 2.86
(1.5107) [(2.5106) 3/100] = 1.57-2.56*3100= 3456/78 = 811/= 149250000. 345678. 81113.
Press these keys to switch between proper and improper fractions. 811/13 = 115/13 I I 81113. 11513. 81113.
The answer to a calculation involving both fractions and decimals is displayed as a decimal.

41/52 78.9

4152*78.9= 62.20961538

Percentage calculations

Press to perform percentage calculations. 12% of as a percentage of plus 15% 1500*12I%= 660d880I%= 2500+15I% = 25% discount on 3500 3500-25I% = 26% of 2200; 26% of 3300; 26% of 3800; 2200**26I%= 3300= 3800= $80 last week; $100 this week: what % is the new value of the old value? 100d80I%= What % is 138gm to 150gm and 129gm to 150gm? 138dd150I%= 129= 92. 86. 125. 572. 858. 988. 180. 75. 375. 2875. 875. 2625.

Converting minutes and seconds to decimal format
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 rightthe first and second digits to the left of decimal point are minutes and the third and subsequent digits seconds.
Press to convert decimal format to sexagesimal format. 142536 I 14.2536 14.42666667 142536
Conversion between angles, radians and grads
45 = 0.785398163 rad = 50 grad 45I I I

RAD GRAD DEG

0.785398163

50. 45.

Trigonometric functions
Press to switch between RAD, DEG and GRAD sin (/6 rad) = cos 635241 = RAD IPd6=s DEG 63.5241 c tan (-35 grad) = GRAD 35t
0.5 63.87805556 0.440283084 -0.612800788 0.597672477 1.732050808 2. 2. 0.760244597 31.39989118 312359.6

DEG DEG

2 sin 45 x cos 65 = DEG 2*45s*65c= cot 30 = 1/tan 30 = 1 sec (/3 rad) = cos (/3 rad) 1 cosec 30 = sin 30 cos tan
DEG 30t RAD IPd3=c 30s RAD 2Id2=c

RAD DEG DEG

10.6104

DEG.6104IT I

Other functions

Hyperbolic functions

sinh 3.6 = tanh 2.5 = cosh 1.5 sinh 1.5 = 3.6s 2.5t 1.5crs=
18.28545536 0.986614298 2.352409615 0.22313016
sinh = solve tanh 4x = 0.x = tan 0.88 = 4

30IS.88ITd4=

4.094622224 0.343941914

Logarithmic functions

log 1.23 (=log10 1.23) = solve 4x = 64 log 64 x = log4 log 456 In 456 = 100.4 + 5 e.3 = 5.6

1.23L 64Ld4L= 456Ldr=

0.089905111 3.

0.434294481

.4I+5*3I= 5.62.3= 123I7= (78-23)12= 312+10I=
2.760821773 52.58143837 1.988647795

1.305111829-21

1231/7 (=7123) = (78 23)

312 + e10 =

553467.4658

Powers and roots

2 + 3 x 5 =
2I+3I*5I= 5I+27I 123+30= 8I
5.287196909 -1.290024053 1023. 40320

5 + -27 =

123 + 302 = 8! (=1 x 2 x 3 x x 7 x 8 ) =

Miscellaneous functions

1.234 + 1.234 = I21.234+ 1.234= I. 13+13= I21d3+ I 1d3= I I. 123m x 456m = 56088m = 56.088km 7.8g 96 = 0.08125g = 81.25mg 123*456= I 7.8d96= I 1.23 2.47 2.468 0.33 3.33-01 6.67-01 0.67 0.666666666 56088. 56.0.08125 81.25 - 03
Polar to rectangular coordinates conversions

Formula: x = r cos y = r sin eg, find the value of x and y when the point P is shown as =60 and the length r=2 in the polar coordinates DEG 2I60I I I 1.

1.732050808

Rectangular to polar coordinates conversions
Formula: r = x2 + y2 = tan-1y/x (-180< 180) eg, find the length r and the angle in radian when the point P is shown as x=1 and y=3 in the rectangular coordinates. RAD 1I3I= I I 2.

1.047197551

( in radian)
Use the M key to set the number base. When you use bases other than 10, you can only enter numbers valid for the baseeg, in binary mode you can only enter 1 and 0. M 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. M sets the mode to octal. M sets the mode to binary. M 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. Conversion of 7FFFFFFF16 to decimal. M7FFFFFFFM Conversion of 12345610 to octal. 123456M Conversion of 11001102 to decimal. M1100110M 102.

22M M 513M

BIN OCT E BIN

10110. 26. 0.

Conversion to binary mode generates an error if the result is greater than 10 digits.

2147483647. 361100.

Binary/octal/decimal/hexadecimal calculations
1238 x ABC16 =37AF416 =22808410 1F2D=788110 =1EC916 M1F2D-M100 M=
101112 + 110102 = 1100012 M1011+1101=

11000.

M123*MABC= M

37AF4. 228084.

7881. 1EC9.
Binary, octal and hexadecimal values

= 334.33.10 = 5168

Fractional parts of calculation results are truncated.

M7654dM12=

334.3333333
1102+4568x78101A16 =39016 =91210 BC16 x (1410 + 6910 =1560410 =3CF416

M110+M456*

M78dM1A= M

390. 912.

Multiplication and division are given priority over addition and subtraction in mixed calculations.

MBC*(M14+69)= M

15604. 3CF4.

Logical operations

&o xX
You can use the following logical operations to compare two numbers. When performing logical operations, keep the following points in mind: 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 0seg, 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. returns the diminished radix complement. Press these keys to perform the respective binary, octal, decimal and hexadecimal logical operations.

1916AND 1A16 = 1816 M19&1A= 12016OR 11012 = 12D16 M120oM1101= M 516XOR 316 = 616 M5X3= 2A16XNOR 5D16 = FFFFFFFF8816 M2AX5D= 1A16 AND 2F16 = A16 M1A&&2F= NOT of 10102 M10110
BIN HEX HEX HEX BIN HEX HEX

100101101.

12d. 6.

FFFFFFFF88.

1111101001.

Radix complement

Press to calculate and display the radix complement of the hexadecimal, octal or binary number currently displayedie, 10000000000-the binary version of the number.
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
Press after each data element. When you press , 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: 3 To enter the results of a calculation as a data item, perform the calculation as you would normally, then press when the answer is displayed. You can amend the data entered into the calculator: To cancel the last entry you made, press before you press. Note that when you press , 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 I.
Using statistical functions on your data
Once you enter a list of data values you can use the following statistical functions: In I I I I I The number of data elements entered Sample standard deviation Population standard deviation Arithmetic mean The sum of each data element The sum of the data elements squared
Find the sample standard deviation of the data 5, and 6. M59136I 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 I, then enter the right number, 58, and.

3.593976442

Using statistics

8. Specifications

Scientific functions/input range
sinx / cosx / tanx sin-1x / cos-1x tan-1x sinhx / coshx tanhx sinh-1x cosh-1x tanh-1x logx / Inx ex 10x yx |x|<4.5x1010 degrees (<25x107rad,<5x1010grad |x|1 |x|<10100 |x|230.2585092 |x|<10100 |x|<5x1099 |x|x<5x1099 |x|<1 10-99x<10100 -10100<x230.2585092 -10100<x<100 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 y<0x : odd number or 1/n (n : integer) 0x<10100 |x|<1050 |x|<10100 |x|<10100(xo) 0x<69 (x: integer) x2 + y2<10100 ||<4.5x1010 degrees (<25x107rad, <5x1010grad) 0r10100 |x|10100 |x|digits Positive: 0x1111111111 Negative: 1000000000x1111111111 Positive: 0x3777777777 Negative: 4000000000x7777777777 Positive: 0x9999999999 Negative: -9999999999x<0 Positive: 0x2540BE3FF Negative: FDABF41C01xFFFFFFFFFF

x x2 3x 1/x n! RECPOL POLREC
DMSDEG DEGDMS Binary Octal Decimal Hexadecimal

Specifications

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 0C40C (32F104F).
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. Dont 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

value in the Xregister and does not affect the stack. New value of variable = Previous value of variable {+, , , } x. For example, suppose you want to reduce the value in A(15) by the number in the Xregister (3, displayed). Press the display.
A. Now A = 12, while 3 is still in

Result: that is, A x

t z y 3

Recall Arithmetic

Recall arithmetic uses ,

, , or to do arithmetic

in the Xregister using a recalled number and to leave the result in the display. Only the Xregister is affected. The value in the variable remains the same and the result replaces the value in the x-register. New x = Previous x {+, , , } Variable For example, suppose you want to divide the number in the Xregister (3, displayed) by the value in A(12). Press
A. Now x = 0.25, while 12 is still in A. Recall arithmetic saves memory in programs: using A (one instruction) uses half as much memory as A, (two instructions).
t z y 0.25 Result: that is, x 12
Example: Suppose the variables D, E, and F contain the values 1, 2, and 3. Use storage arithmetic to add 1 to each of those variables.
Stores the assumed values into the variable. Adds1 to D, E, and F.

D E F D E F D E F

Displays the current value of D.
Clears the VIEW display; displays Xregister again.
Suppose the variables D, E, and F contain the values 2, 3, and 4 from the last example. Divide 3 by D, multiply it by E, and add F to the result.

3 D E.

Calculates 3 D. 3 D E + F.
Exchanging x with Any Variable
key allows you to exchange the contents of x (the displayed X
register) with the contents of any variable. Executing this function does not affect the Y, Z, or Tregisters.
Stores 12 in variable A. Displays x. Exchanges contents of the Xregister and variable A. Exchanges contents of the Xregister and variable A.

A A A

t z y 12
The Variables "I" and "J"
There are two variables that you can access directly: the variables I and J. Although they store values as other variables do, I and J are special in that they can be used to refer to other variables, including the statistical registers, using the (I) and (J) commands. (I) is found on the
key, while (J) is on the key. This is a
programming technique called indirect addressing that is covered under Indirectly Addressing Variables and Labels in chapter 14.

Clears memory.

() ()
Selects Equation mode. Starts the equation.

_ G _

Terminates the equation and displays the left end. Checksum and length.
g (acceleration due to gravity) is included as a variable so you can change it for different units (9.8 m/s2 or 32.2 ft/s2 ). Calculate how many meters an object falls in 5 seconds, starting from rest. Since Equation mode is turned on and the desired equation is already in the display, you can start solving for D:

_ value value value

Prompts for unknown variable. Selects D; prompts for V. Stores 0 in V; prompts for T. Stores 5 in T; prompts for G. Stores 9.8 in G; solves for D.
Try another calculation using the same equation: how long does it take an object to fall 500 meters from rest?
Displays the equation. Solves for T; prompts for D. Stores 500 in D; prompts for V. Retains 0 in V; prompts for G. Retains 9.8 in G; solves for T.
Example: Solving the Ideal Gas Law Equation. The Ideal Gas Law describes the relationship between pressure, volume, temperature, and the amount (moles) of an ideal gas: PV=NRT where P is pressure (in atmospheres or N/m2), V is volume (in liters), N is the number of moles of gas, R is the universal gas constant (0.0821 literatm/moleK or 8.314 J/moleK), and T is temperature (Kelvins: K=C + 273.1). Enter the equation:
Selects Equation mode and starts the equation.
_ Terminates and displays the equation. Checksum and length.
A 2liter bottle contains 0.005 moles of carbon dioxide gas at 24C. Assuming that the gas behaves as an ideal gas, calculate its pressure. Since Equation mode is turned on and the desired equation is already in the display, you can start solving for P:

value value value value

Solves for P; prompts for V. Stores 2 in V; prompts for N. Stores.005 in N; prompts for R. Stores.0821 in R; prompts for T. Calculates T (Kelvins). Stores 297.1 in T; solves for P in atmospheres.
A 5liter flask contains nitrogen gas. The pressure is 0.05 atmospheres when the temperature is 18C. Calculate the density of the gas (N 28/V, where 28 is the molecular weight of nitrogen).
Displays the equation. Solves for N; prompts for P. Stores.05 in P; prompts for V. Stores 5 in V; prompts for R. Retains previous R; prompts for T. Calculates T (Kelvins).

_ _

Selects Equation mode. Starts the equation. The closing right parenthesis is required in this case. Terminates the equation. Checksum and length. Leaves Equation mode.

X X

Now integrate this function with respect to x (that is, X) from zero to 2 (t = 2).
Selects Radians mode. Enters limits of integration (lower first). Displays the current equation. Calculates the result for Si(2).

9 () X X

Accuracy of Integration
Since the calculator cannot compute the value of an integral exactly, it approximates it. The accuracy of this approximation depends on the accuracy of the integrand's function itself, as calculated by your equation. This is affected by round off error in the calculator and the accuracy of the empirical constants. Integrals of functions with certain characteristics such as spikes or very rapid oscillations might be calculated inaccurately, but the likelihood is very small. The general characteristics of functions that can cause problems, as well as techniques for dealing with them, are discussed in appendix E.

Specifying Accuracy

The display format's setting (FIX, SCI, ENG, or ALL) determines the precision of the integration calculation: the greater the number of digits displayed, the greater the precision of the calculated integral (and the greater the time required to calculate it). The fewer the number of digits displayed, the faster the calculation, but the calculator will presume that the function is accurate to the only number of digits specified. To specify the accuracy of the integration, set the display format so that the display shows no more than the number of digits that you consider accurate in the integrand's values. This same level of accuracy and precision will be reflected in the result of integration. If Fractiondisplay mode is on (flag 7 set), the accuracy is specified by the previous display format.

Interpreting Accuracy

After calculating the integral, the calculator places the estimated uncertainty of that integral's result in the Yregister. Press
to view the value of the uncertainty.
For example, if the integral Si(2) is 1.6054 0.0002, then 0.0002 is its uncertainty.
Example: Specifying Accuracy. With the display format set to SCI 2, calculate the integral in the expression for Si(2) (from the previous example).
Sets scientific notation with two decimal places, specifying that the function is accurate to two decimal places. Rolls down the limits of integration from the Zand Tregisters into the Xand Yregisters. Displays the current Equation. The integral approximated to two decimal places. The uncertainty of the approximation of the integral.

, and then enter the independent variable (the first.
() to clear existing statistical data. 2. Key in the yvalue first and press. 3. Key in the corresponding xvalue and press.
4. The display shows n, the number of statistical data pairs you have accumulated. 5. Continue entering x, ypairs. n is updated with each entry. To recall an xvalue to the display immediately after it has been entered, press
Correcting Errors in Data Entry
If you make a mistake when entering statistical data, delete the incorrect data and add the correct data. Even if only one value of an x, ypair is incorrect, you must delete and reenter both values.
To correct statistical data: 1. Reenter the incorrect data, but instead of pressing deletes the value(s) and decrements n. 2. Enter the correct value(s) using

, press . This

. to retrieve
If the incorrect values were the ones just entered, press them, then press
to delete them. (The incorrect yvalue was still in the Y
register, and its xvalue was saved in the LAST X register.) After deleting the incorrect statistical data, calculator will display the value of Y-register in line 1 and value of n in line 2. Example: Key in the x, yvalues on the left, then make the corrections shown on the right:

Initial x, y

20, 4 400, 6

Corrected x, y

20, 5 40, 6
Clears existing statistical data. Enters the first new data pair. Display shows n, the number of data pairs you entered. Brings back last xvalue. Last y is still in Yregister. Deletes the last data pair. Reenters the last data pair. Deletes the first data pair.
Reenters the first data pair. There is still a total of two data pairs in the statistics registers.

Statistical Calculations

Once you have entered your data, you can use the functions in the statistics menus.

Statistics Menus Menu

The linearregression menu: linear estimation

x ,y

and curvefitting . See ''Linear
Regression'' later in this chapter. The mean menu: below. The standarddeviation menu: . See "Sample Standard Deviation" and "Population Standard Deviation" later in this chapter. The summation menu: . See "Summation Statistics" later in this chapter.

. See "Mean"

Mean is the arithmetic average of a group of numbers. Press Press
( ) for the mean of the xvalues. ( ) for the mean of the yvalues.
Press ( ) for the weighted mean of the xvalues using the yvalues as weights or frequencies. The weights can be integers or non integers.
Example: Mean (One Variable). Production supervisor May Kitt wants to determine the average time that a certain process takes. She randomly picks six people, observes each one as he or she carries out the process, and records the time required (in minutes): 15.5 12.5 9.25 12.0 10.0 8.5

Statistical Operations 12-13
12-14 Statistical Operations

Part 2

Simple Programming
Part 1 of this manual introduced you to functions and operations that you can use manually, that is, by pressing a key for each individual operation. And you saw how you can use equations to repeat calculations without doing all of the keystrokes each time. In part 2, you'll learn how you can use programs for repetitive calculations calculations that may involve more input or output control or more intricate logic. A program lets you repeat operations and calculations in the precise manner you want. In this chapter you will learn how to program a series of operations. In the next chapter, "Programming Techniques," you will learn about subroutines and conditional instructions. Example: A Simple Program. To find the area of a circle with a radius of 5, you would use the formula A = r2 and press RPN mode: 5 ALG mode: 5
to get the result for this circle, 78.5398. But what if you wanted to find the area of many different circles? Rather than repeat the given keystrokes each time (varying only the "5" for the different radii), you can put the repeatable keystrokes into a program:

RPN mode

ALG mode
This very simple program assumes that the value for the radius is in the X register (the display) when the program starts to run. It computes the area and leaves it in the Xregister. In RPN mode, to enter this program into program memory, do the following:

Keys: (In RPN mode)

Clears memory. Activates Programentry mode (PRGM annunciator on). Resets program pointer to PRGM TOP. (Radius)2 Area = x2 Exits Programentry mode.

() ()

Try running this program to find the area of a circle with a radius of 5:
This sets the program to its beginning. The answer!

Keys: (In ALG mode)

In ALG mode, to enter this program into program memory, do the following:
Clears memory. Activates Programentry mode (PRGM annunciator on).
Resets program pointer to PRGM TOP. Area = x2 Exits Programentry mode.
This sets the program to its beginning. Stores 5 into X

The answer!

We will continue using the above program for the area of a circle to illustrate programming concepts and methods.

Designing a Program

The following topics show what instructions you can put in a program. What you put in a program affects how it appears when you view it and how it works when you run it.

Selecting a Mode

Programs created and saved in RPN mode should be edited and executed in RPN mode, and programs or steps created and saved in ALG mode should be edited and executed in ALG mode. If not, the result may be incorrect.
Program Boundaries (LBL and RTN)

13-14 Simple Programming

To cancel the INPUT prompt, press. The current value for the variable remains in the Xregister. If you press to resume the program, the canceled INPUT prompt is repeated. If you press during digit entry, it clears the number to zero. Press again to cancel the INPUT prompt.
Using VIEW for Displaying Data
The programmed VIEW instruction ( variable ) stops a running program and displays and identifies the contents of the given variable, such as This is a display only, and does not copy the number to the Xregister. If Fraction display mode is active, the value is displayed as a fraction. Pressing
copies this number to the Xregister.
If the number is wider than 14 characters, such as binary, complex, vector numbers, pressing and displays the rest. Pressing Pressing Press
(or ) erases the VIEW display and shows the Xregister.
clears the contents of the displayed variable.

to continue the program.

If you don't want the program to stop, see "Displaying Information without Stopping" below. For example, see the program for "Normal and InverseNormal Distributions" in chapter 16. Lines T015 and T016 at the end of the T routine display the result for X. Note also that this VIEW instruction in this program is preceded by a RCL instruction. The RCL instruction is not necessary, but it is convenient because it brings the VIEWed variable to the Xregister, making it available for manual calculations. (Pressing
while viewing a VIEW display would have the same effect.) The
other application programs in chapters 16 and 17 also ensure that the VIEWed variable is in the Xregister as well.

Simple Programming 13-15

Using Equations to Display Messages
Equations aren't checked for valid syntax until they're evaluated. This means you can enter almost any sequence of characters into a program as an equation you
to start the equation. Press number and math keys to get numbers and symbols. Press before each letter. Press to end the equation.
enter it just as you enter any equation. On any program line, press If flag 10 is set, equations are displayed instead of being evaluated. This means you can display any message you enter as an equation. (Flags are discussed in detail in chapter 14.) When the message is displayed, the program stops press to resume execution. If the displayed message is longer than 14 characters, the annunciator turns on when the message is displayed. You can then use and

or ).

2. Key in the new instruction; it is inserted after the currently displayed line. For example, if you wanted to insert a new line between lines A004 and A005 of a program, you would first display line A004, then key in the instruction or instructions. Subsequent program lines, starting with the original line A005, are moved down and renumbered accordingly. To edit operand, expression or equation in a program line: 1. Locate or display the program line that you want to edit.
or to start editing the program line. These turn on the _
editing cursor, but do not delete anything in the program line
key actives the cursor to the left of the program line key actives the cursor to the end of the program line

13-20 Simple Programming

3. Moving the cursor_ and press
repeatedly to delete the unwanted
number or function, then retype the rest of the program line. (After pressing
, Undo function is active)
Notice: 1. When the cursor is active in the program line, disabled. 2. When you are editing a program line (cursor active), and the program line is

or key will be

will have no effect. If you want to erase the program line, press and the program line will be erased. 3. You can use and key to review long program lines and
empty, using without editing it. 4. In ALG mode, program line. 5. An equation can be editing in any mode no matter which mode it was entered in.
can not be used as a function, it is used to validate a

Program Memory

Viewing Program Memory
Pressing toggles the calculator into and out of program entry (PRGM annunciator on, program lines displayed). When Programentry mode is active, the contents of program memory are displayed. Program memory starts at . The list of program lines is circular, so you can wrap the program pointer from the bottom to the top and reverse. While program entry is active, there are four ways to change the program pointer (the displayed line):
and allows you to move from label to label. If no labels
are defined, It will move to the top or bottom of the program. To move more than one line at a time ("scrolling"), continue to hold the or key.

Simple Programming 13-21

Press Press
to move the program pointer to . label nnn to move to a specific line.
If Programentry mode is not active (if no program lines are displayed), you can also move the program pointer by pressing

label line number.

Canceling Programentry mode does not change the position of the program pointer.

Memory Usage

If during program entry you encounter the message , then there is not enough room in program memory for the line you just tried to enter. You can make more room available by clearing programs or other data. See "Clearing One or More Programs" below, or "Managing Calculator Memory" in appendix B.

Display INVALID (I), because address 170 is undefined
If you want to recall the value from an undefined storage address, the error message will be shown. (See A014) The calculator allocates memory for variable 0 to the last non-zero variable. It is important to store 0 in variables after using them in order to release the memory. Each allocated indirect register uses 37 bytes of program memory. There is a maximum of 800 variables.
14-24 Programming Techniques
Solving and Integrating Programs

Solving a Program

In chapter 7 you saw how you can enter an equation it's added to the equation list and then solve it for any variable. You can also enter a program that calculates a function, and then solve it for any variable. This is especially useful if the equation you're solving changes for certain conditions or if it requires repeated calculations. To solve a programmed function: 1. Enter a program that defines the function. (See "To write a program for SOLVE" below.)
2. Select the program to solve: press
label. (You can skip this step if variable.
you're resolving the same program.) 3. Solve for the unknown variable: press
Notice that FN= is required if you're solving a programmed function, but not if you're solving an equation from the equation list. To halt a calculation, press use

or and the message will

appear in line 2. The current best estimate of the root is in the unknown variable;
to view it without disturbing the stack. To resume the calculation, press.
To write a program for SOLVE: The program can use equations and ALG or RPN operations in whatever combination is most convenient.
Begin the program with a label. This label identifies the function that you want SOLVE to evaluate (label).
2. Include an INPUT instruction for each variable, including the unknown. INPUT instructions enable you to solve for any variable in a multivariable function. INPUT for the unknown is ignored by the calculator, so you need to write only one program that contains a separate INPUT instruction for every variable (including the unknown). If you include no INPUT instructions, the program uses the values stored in the variables or entered at equation prompts. 3. Enter the instructions to evaluate the function. A function programmed as a multiline RPN or ALG sequence must be in the form of an expression that goes to zero at the solution. If your equation is f(x) = g(x), your program should calculate f(x) g(x). "=0" is implied. A function programmed as an equation can be any type of equation equality, assignment, or expression. The equation is evaluated by the program, and its value goes to zero at the solution. If you want the equation to prompt for variable values instead of including INPUT instructions, make sure flag 11 is set. 4. End the program with a RTN. Program execution should end with the value of the function in the Xregister. Example: Program Using ALG. Write a program using ALG operations that solves for any unknown in the equation for the "Ideal Gas Law." The equation is: P x V= N x R x T where P = Pressure (atmospheres or N/m2). V = Volume (liters). N = Number of moles of gas. R = The universal gas constant (0.0821 literatm/moleK or 8.314 J/moleK). T = Temperature (kelvins; K = C + 273.1).

Displays, prompts for, and, if changed, stores xvalue in X. If flag 0 is set. Branches to K001 Branches to M001 Stores y value in Y.
Displays, prompts for, and, if changed, stores yvalue in Y. If flag 0 is set. Branches to O001 Branches to N001 Stores x in X for next loop. Loops for another estimate. Checksum and length: C3B
This subroutine calculates y for the straightline model.

Calculates y = MX + B.

Returns to the calling routine. Checksum and length: 9688 15
This subroutine calculates x for the straightline model. Calculates x =(Y B) M. Returns to the calling routine. Checksum and length: 9C0F 15
This subroutine calculates y for the logarithmic model.
Calculates y = M In X + B.
Returns to the calling routine.
Checksum and length: 889C 18
This subroutine calculates x for the logarithmic model.
Calculates x = e(Y B) M Returns to the calling routine. Checksum and length: 0DBE 18
This subroutine calculates y for the exponential model.

Calculates y = BeMX.

Branches to M005 Checksum and length:
This subroutine calculates x for the exponential model.

Checksum and length:

Calculates x = (ln (Y B)) M. Goes to N005
This subroutine calculates y for the power model.
Calculates Y= B (XM). Goes to K005 Checksum and length: 11B3 18
This subroutine calculates x for the power model.
Calculates x = (Y/B ) 1/M Goes to O005 Checksum and length: 8524 21
Determines if D001 or B001 should be run If flag 1 is set. Executes D001 Executes B001 Goes to Y006
Checksum and length: 4BFA 15 Determines if C001 or A001 should be run If flag 1 is set. Executes C001 Executes A001 Goes to Y006
Checksum and length: 1C4D 15 Determines if J001 or H001 should be run If flag 1 is set. Executes J001 Executes H001 Goes to Y011
Checksum and length: 0AA Determines if I001 or G001 should be run If flag 1 is set.
Executes I001 Executes G001 Goes to Y011 Checksum and length: 666D 15
Flags Used: Flag 0 is set if a natural log is required of the X input. Flag 1 is set if a natural log is required of the Y input. If flag 1 is set in routine N, then I001 is executed. If flag 1 is clear, G001 is executed. Program instructions: 1. Key in the program routines; press

when done.

and select the type of curve you wish to fit by pressing:
S for a straight line; L for a logarithmic curve; E for an exponential curve; or P for a power curve. 3. Key in xvalue and press. 4. Key in yvalue and press.

Calculates S 2. Stores result temporarily for inverse routine.
Adds half the area under the curve since we integrated using the mean as the lower limit. Returns to the calling routine. Checksum and length: This subroutine calculates the integrand for the normal function

e (( X M) S )

16-14 Statistics Programs
Returns to the calling routine. Checksum and length: B3EB 31
Flags Used: None. Remarks: The accuracy of this program is dependent on the display setting. For inputs in the area between 3 standard deviations, a display of four or more significant figures is adequate for most applications. At full precision, the input limit becomes 5 standard deviations. Computation time is significantly less with a lower number of displayed digits. In routine Q, the constant 0.5 may be replaced by 2 and
You do not need to key in the inverse routine (in routines I and T) if you are not interested in the inverse capability. Program Instructions: 1. Key in the program routines; press

when done. (If the

3. After the prompt for M, key in the population mean and press mean is zero, just press
Statistics Programs 16-15
4. After the prompt for S, key in the population standard deviation and press
. (If the standard deviation is 1, just press.)
5. To calculate X given Q(X), skip to step 9 of these instructions. 6. To calculate Q(X) given X, 7. displayed. 8. To calculate Q(X) for a new X with the same mean and standard deviation, press

D. The result, Q(X), is

After the prompt, key in the value of X and press
and go to step 7. I. The result, X, is
9. To calculate X given Q(X), press displayed.
10. After the prompt, key in the value of Q(X) and press
11. To calculate X for a new Q(X) with the same mean and standard deviation, press

and go to step 10.

Variables Used: D M Q S T X Example 1: Your good friend informs you that your blind date has "3" intelligence. You interpret this to mean that this person is more intelligent than the local population except for people more than three standard deviations above the mean. Suppose that you intuit that the local population contains 10,000 possible blind dates. How many people fall into the "3" band? Since this problem is stated in terms of standard deviations, use the default value of zero for M and 1 for S. Dummy variable of integration. Population mean, default value zero. Probability corresponding to the uppertail area. Population standard deviation, default value of 1. Variable used temporarily to pass the value S 2 to the inverse program. Input value that defines the left side of the uppertail area.
Starts the initialization routine.
16-16 Statistics Programs

value

Accepts the default value of zero for M. Accepts the default value of 1 for S. Starts the distribution program and prompts for X. Enters 3 for X and starts computation of Q(X). Displays the ratio of the population smarter than everyone within three standard deviations of the mean. Multiplies by the population. Displays the approximate number of blind dates in the local population that meet the criteria.

Since your friend has been known to exaggerate from time to time, you decide to see how rare a "2" date might be. Note that the program may be rerun simply by pressing
Resumes program. Enters Xvalue of 2 and calculates Q(X). Multiplies by the population for the revised estimate.

Example 2:

The mean of a set of test scores is 55. The standard deviation is 15.3. Assuming that the standard normal curve adequately models the distribution, what is the probability that a randomly selected student scored at least 90? What is the score that only 10 percent of the students would be expected to have surpassed? What would be the score that only 20 percent of the students would have failed to achieve?
Statistics Programs 16-17

value

Starts the initialization routine. Stores 55 for the mean. Stores 15.3 for the standard deviation. Starts the distribution program and prompts for X. Enters 90 for X and calculates Q(X).
Thus, we would expect that only about 1 percent of the students would do better than score 90.
Starts the inverse routine. Stores 0.1 (10 percent) in Q(X) and calculates X. Resumes the inverse routine. Stores 0.8 (100 percent minus 20 percent) in Q(X) and calculates X.
Grouped Standard Deviation
The standard deviation of grouped data, Sxy, is the standard deviation of data points x1, x2,. , xn, occurring at positive integer frequencies f1, f2,. , fn.

xi 2f i

( xif i) 2 fi ( fi ) 1
16-18 Statistics Programs
This program allows you to input data, correct entries, and calculate the standard deviation and weighted mean of the grouped data.
Start grouped standard deviation program. Clears statistics registers (-27 through -32). Clears the count N. Checksum and length: E5BC 13 Input statistical data points. Stores data point in X. Stores datapoint frequency in F. Enters increment for N. Recalls datapoint frequency fi. Checksum and length: Accumulate summations. Stores index for register -27. Updates

in register -27.

Stores index for register -28. Updates

x i fi

in register -28.
Stores index for register -30.
Statistics Programs 16-19
Updates xi 2fi in register -30. Increments (or decrements) N. Displays current number of data pairs. Goes to label line numberI for next data input. Checksum and length: F6CB 84 Calculates statistics for grouped data. Grouped standard deviation. Displays grouped standard deviation. Weighted mean. Displays weighted mean. Goes back for more points. Checksum and length: DAF Checksum Undo dataentry error. Enters decrement for N. Recalls last data frequency input. Changes sign of fi.

The catalog of programs ( () ) indicates no program labels stored. No solution could be found for this system of linear equations. Multiple solutions have been found for this system of linear equations.
SOLVE (include EQN and PGM mode)cannot find the root of the equation using the current initial guesses (see page ). These conditions include: bad guess, solution not found, point of interest, left unequal to right. A SOLVE operation executed in a program does not produce this error; the same condition causes it instead to skip the next program line (the line following the instruction variable). Warning (displayed momentarily); the magnitude of a result is too large for the calculator to handle. The calculator returns 9.99999999999E499 in the current display format. (See "Range of Numbers and Overflow" on page.) This condition sets flag 6. If flag 5 is set, overflow has the added effect of halting a running program and leaving the message in the display until you press a key. Indicates the "top" of program memory. The memory scheme is circular, so is also the "line" after the last line in program memory.
The calculator is running an equation or program (other than a SOLVE or FN routine). Attempted to execute variable or d variable without a selected program label. This can happen the first time that you use SOLVE or FN after the message , or it can happen if the current label no longer exists. A running program attempted to select a program label (label) while a SOLVE operation was running. A running program attempted to solve a program while a SOLVE operation was running. A running program attempted to integrate a program while a SOLVE operation was running. The calculator is solving an equation or program for its root. This might take a while. Attempted to calculate the square root of a negative number.
Statistics error: Attempted to do a statistics calculation with n = 0. Attempted to calculate sx sy, x , y , m, r, or b with n = 1. Attempted to calculate r, x or xw with xdata only (all yvalues equal to zero). Attempted to calculate x , y , r, m, or b with all x values equal.
A syntax error was detected during evaluation of an expression, equation,, or ". Pressing or
clears the error message and allows you to correct
the error. The magnitude of the number is too large to be converted to HEX, OCT, or BIN base; the number must be in the range 34,359,738,368 n 34,359,738,367. A running program attempted an 21st nested label. (Up to 20 subroutines can be nested.) Since SOLVE and FN each uses a level, they can also generate this error. The condition checked by a test instruction is true. (Occurs only when executed from the keyboard.)

27 137

() CL CLVARS CLx

(4) () ()

Clears statistics registers. Clears all variables to zero. Clears x (the Xregister) to zero.

CLVARx

Clears indirect variables whose address is greater than the x address to zero. CLSTK CM nCr
() Clears all stack levels to zero. Converts inches to

centimeters.

x Combinations of n items
taken r at a time. Returns n! (r! (n r)!).

COS COSH

Cosine. Returns cos x. Hyperbolic
cosine. Returns cosh x. Accesses the 41 physics constants.

413 121

d DEC DEG DEG
() indicates a decimal number ()

Selects Decimal mode.

Selects Degrees angular mode.

Radians to degrees.

Returns (360/2) x. Displays menu to set the display format, radix ( or ), thousand separator, and display format of complex number.

DSE variable

Decrement, Skip if Equal or less. For control number ccccccc.fffii stored in a variable, subtracts ii (increment value) from ccccccc (counter value) and, if the result fff (final value), skips the next program line.
Begins entry of exponents and adds "E" to the number being entered. Indicates that a power of 10 follows.
Selects Engineering display with n digits following the first digit (n = 0 through 11).

@and2

Causes the exponent display for the number being displayed to change in multiple of 3. Separates two numbers keyed in sequentially; completes equation entry; evaluates the displayed equation (and stores result if appropriate).
Copies x into the Yregister, lifts y into the Zregister, lifts z into the T register, and loses t.

ex EXP

Activates or cancels (toggles) Equationentry mode.

Natural exponential.

Returns e raised to the x power.
Returns e raised to the specified power.

Converts C to F.

Turns on and off Fractiondisplay mode.

8 () n

Selects Fixed display with n decimal places: 0 n 11. Displays the menu to set, clear, and test flags.

FN = label

label
Selects labeled program as the current function (used by SOLVE and FN).

() Fractional part

If flag n (n = 0 through 11) is set, executes the next program line; if flag n is clear, skips the next program line.

GAL GRAD

Converts liters to gallons. 9 ()Sets Grads angular mode.