(hold)

Shows full precision until you release
T he HP 32SII allows you to type in and display fractions, and to perform math operations on them. Fractions are real numbers of the form
a b/c where a, b, and c are integers; 0 b c; and the denominator (c) must be in the range 2 through 4095.

Entering Fractions

Fractions can be entered onto the stack at any time:. (The first 1. Key in the integer part of the number and press separates the integer part of the number from its fractional part.) 2. Key in the fraction numerator and press again. The second separates the numerator from the denominator. 3. Key in the denominator, then press or a function key to
terminate digit entry. The number or result is formatted according to the current display format. The a b/c symbol under the twice for fraction entry. key is a reminder that the key is used
For example, to enter the fractional number 12 3/8, press these keys:

The manner. _

Enters the integer part of the number. key is interpreted in the normal
Enters the numerator of the fraction (the number is still displayed in decimal form). _ The calculator interprets the second as a fraction and separates the numerator from denominator.
Ap pe nds the denominator of the fraction. Terminates digit entry; displays the number in the current display format.
If the number you enter has no integer part (for example, 3/8), just start the number without an integer.

also works.)

Enters no integer part. (3 8
Terminates digit entry; displays the number in the current display format (FIX 4).

Displaying Fractions

Press to switch between Fractiondisplay mode and the current decimal display mode.
Displays characters as you key them in. Terminates digit entry; displays the number in the current display format. Displays the number as a fraction.
Now add 3/4 to the number in the Xregister (12 3/8):
Displays characters as, you key them Adds the numbers in the X and Yregisters; displays the result as a fraction. Switches to current decimal display format.
Refer to chapter 5, "Fractions," for more information about using fractions.

Messages

The calculator responds to certain conditions or keystrokes by displaying a message. The symbol comes on to call your attention to the message. To clear a message, press or. To clear a message and perform another function, press any other key. If no message appears but does, you have pressed an inactive key (a key that has no meaning in the current situation, such as in Binary mode). All displayed messages are explained in appendix E, "Messages."

Calculator Memory

The HP 32SII has 384 bytes of memory in which you can store any combination of data (variables, equations, or program lines). The memory requirements of specific activities are given under "Managing Calculator Memory" in appendix B.

Clearing the XRegister

Pressing { } always clears the Xregister to zero; it is also used to program this instruction. The key, in contrast, is contextsensitive. It. either clears or cancels the current display, depending on the situation: it acts like { } only when the Xregister is displayed. also acts like { } when the Xregister is displayed and digit entry is terminated (no cursor present). It cancels other displays: menus, labeled numbers, messages, equation entry, and program entry.

Reviewing the stack

R (Roll Down) The (roll down) key lets you review the entire contents of the stack by "rolling" the contents downward, one register at a time. You can see each number when it enters the Xregister. Suppose the stack is filled with 1, 2, 3, 4 (press 1 4. Pressing four times rolls the numbers all the way around and back to where they started:
What was in the Xregister rotates into the Tregister, the contents of the Tregister rotate into the Zregister, etc. Notice that only the centents of the registers are rolled the registers themselves maintain their positions, and only the Xregister's contents are displayed. R (Roll Up) except that it "rolls" the
The (roll up) key has a similar function to stack contents upward, one register at a time.
The contents of the Xregister rotate into the Yregister; what was in the Tregister rotates into the Xregister, and so on.
Exchanging the X and YRegisters in the Stack
Another key that manipulates the stack contents is (x exchange y). This key swaps the contents of the X and Yregisters without affecting the rest of the stack. Pressing twice restores the original order of the X and Yregister contents. The function is used primarily for two purposes: To view the contents of the Yregister and then return them to y (press twice). Some functions yield two results: one in the Xregister and one in the Yregister. For example, converts rectangular coordinates in the X and Yregisters into polar coordinates in the X and Yregisters. To swap the order of numbers in a calculation. For example, one way to calculate 9 (13 8): Press 9 The keystrokes to calculate this expression from lefttoright are: 8 Note
Always make sure that there are no more than four numbers in the stack at any given time the contents of the Tregister (the top register) will be lost whenever a fifth number is entered.
ArithmeticHow the Stack Does It
The contents of the stack move up and down automatically as new numbers enter the Xregister (lifting the stack) and as operators combine two numbers in the X and Yregisters t o produce one new number in the Xregister (dropping the stack). Suppose the stack is filled with the numbers 1, 2, 3, and 4. See how the stack drops and lifts its contents while calculating

Replicates Tregister

T 1.5 Z Y X 1

1.5 1.5 1.5 1.1

1.5 1.5 1.2

1.5 1.5 1.3

1.5 1.5 1.4

1.5 1.5 1.5

1. 2. 3. 4. 5.
Fills the stack with the growth rate. Keys in the initial population. Calculates the population after 1 day. Calculates the population after 2 days. Calculates the population after 3 days.

How CLEAR x Works

Clearing the display (Xregister) put zero in the Xregister. The next number you key in (or recall writes over this zero. There are three ways to clear the contents of the Xregister, that is, to clear x: 1. Press 2. Press 3. Press Note these exceptions: During program entry, deletes the currentlydisplayed program line and cancels program entry. During digit entry, backspaces over the displayed number. ), pressing If the display shows a labeled number (such as
{ } (Mainly used during program entry.)
cancel that display and shows the Xregister. displays the cursor at the end the backspaces over the displayed equation,
When viewing an equation, equation to allow for editing. During equation entry, one function at a time.
For example, if you intended to enter 1 and 3 but mistakenly entered 1 and 2, this what you should do to correct your error:

T Z Y X 1

1. 2. 3. 4. 5. 3
Lifts the stack Lift the stack and replicates the Xregister. Overwrites the Xregister. Clears x by overwriting it with zero. Overwrites x (replaces the zero.)

The LAST X Register

The LAST X register is a companion to the stack: it holds the number that was in the Xregister before the last numeric function was executed. (A numeric function is an operation that produces a result from another number or numbers, such as.) Pressing returns this value into the Xregister. This ability to retrieve the "last x" has two main uses: 1. Correcting errors. 2. Reusing a number in a calculation.
See appendix B for a comprehensive list of the functions that save x in the LAST X register.
Correcting Mistakes with LAST X
Wrong OneNumber Function If you execute the wrong onenumber function, use the number so you can execute the correct function. (Press want to clear the incorrect result, from the stack.) to retrieve first if you
and don't cause the stack to drop, you can Since recover from these functions in the same manner as from onenumber functions. Example: Suppose that you had just computed In 4.7839 (3.879 105) and wanted to find its square root, but pressed by mistake. You don't have to start over! To find the correct result, press. Mistakes with a Twonumber operation If you make a mistake with a twonumber operation, ( or ), you can correct it by using twonumber function ( or , or , or , , , , and inverse of the ).
1. Press to recover the second number (x just before the operation). 2. Execute the inverse operation. This returns the number that was originally first. The second number is still in the LAST X register. Then: If you had used the wrong function, press again to restore the original stack contents. Now execute the correct function. If you had used the wrong second number, key in the correct one and execute the function. If you had used the wrong first number, key in the correct first number, press to recover the second number, and execute the function again. (Press first if you want to clear the incorrect result from the stack.) Example:

Calculates (3 + 10) first. Puts 2 before 13 so the division is correct: 2 13.
Calculate 4 [(14 + (7 3) 2] :
Calculates (7 3). Calculates denominator. Puts 4 before 33 in preparation for division. Calculates 4 33, the answer.
Problems that have multiple parentheses can be solved in the same manner using the automatic storage of intermediate results. For example, to solve (3 + 4) (5 + 6) on paper, you would first calculate the quantity (3 + 4). Then you would calculate (5 + 6). Finally, you would multiply the two intermediate results to get the answer.
Work through the problem the same way with the HP 32SII, except that you don't have to write down intermediate answersthe calculator remembers them for you.
First adds (3+4) Then adds (5+6) Then multiplies the intermediate answers together for the final answer.

Exercises

Calculate:
(16.3805x 5) = 181.0000 0.05
Solution: 16.3805 Calculate: 5.05
[(2 + 3) (4 + 5)] + [(6 + 7) (8 + 9) = 21.5743

Solution: 8 9

Calculate: (10 5) [(17 12) 4] = 0.2500 Solution: 17 or 4

Order of Calculation

We recommend solving chain calculations by working from the innermost parentheses outward. However, you can also choose to work problems in a lefttoright order. For example, you have already calculated: 4 [14 + (7 3) 2] by starting with the innermost parentheses (7 3) and working outward, just as you would with pencil and paper. The keystrokes were 4 If you work the problem from lefttoright, press 2.
This method takes one additional keystroke. Notice that the first intermediate result is still the innermost parentheses (7 3). The advantage to working a problem lefttoright is that you don't have to use to reposition operands for nomcommutaiive functions ( and ). However, the first method (starting with the innermost parentheses) is often preferred because: It takes fewer keystrokes. It requires fewer registers in the stack. Note When using the lefttoright method, be sure that no more than four intermediate numbers (or results) will be needed at one time (the stack can hold no more than four numbers).
The above example, when solved lefttoright, needed all registers in the stack at one point:
Saves 4 and 14 as intermediate numbers in the stack.
At this point the stack is full with numbers for this calculation. Intermediate result. Intermediate result.
Intermediate result. Final result.

More Exercises

Practice using RPN by working through the following problems: Calculate: (14 + 12) (18 12) (9 7) = 78.0000 A Solution: 9 7

Fractional part. Removes the integer part of x and replaces it with zeros. (For example, the fractional part of 14.2300 is 0.2300)
Absolute value. Replaces x with its absolute value.
The RND function ( ) rounds x internally to the number of digits specified by the display format. (The internal number is represented by 12 digits.) Refer to chapter 5 for the behavior of RND in Fractiondisplay mode.

Names of Function

You might have noticed that the name of a function appears in the display when you press and hold the key to execute it. (The name remains displayed for as long as you hold the key down.) For instance, while pressing , the display shows. "SQRT" is the name of the function as it will appear in program lines (and usually in equations also).
"Fractions" in chapter 1 introduces the basics about entering, displaying, and calculating with fractions: To enter a fraction, press twiceafter the integer part, and between the numerator and denominator. To enter 2 3/8, press 8. To 5/8, press enter or 5 8. To turn Fractiondisplay mode on and off, press. When you turn off Fractiondisplay mode, the display goes back to the previous display format. (FIX, SCI, ENG, and ALL also turn off Fractiondisplay mode.) Functions work the same with fractions as with decimal numbersexcept for RND, which is discussed later in this chapter. This chapter gives more information about using and displaying fractions.
You can type almost any number as a fraction on the keyboard including an improper fraction (where the numerator is larger than the denominator). However, the calculator displays if you disregard these two restrictions. The integer and numerator must not contain more than 12 digits total. The denominator must not contain more than 4 digits.
Turns on Fractiondisplay mode. Enters 1.5; shown as a fraction. Enters 1 3/4. Displays x as a decimal number. Displays x as a fraction.
If you didn't get the same results as the example, you may have accidentally changed how fractions are displayed. (See "Changing the Fraction Display" later in this chapter.) The next topic includes more examples of valid and invalid input fractions. You can type fractions only if the number base is 10 the normal number base. See chapter 10 for information about changing the number base.

Fractions in the Display

How You Can Use Equations
You can use equations on the HP 32SII in several way: For specifying an equation to evaluate (this chapter). For specifying an equation to solve for unknown values (chapter 7). For specifying a function to integrate (chapter 8). Example: Calculating with an Equation. Suppose you frequently need to determine the volume of a straight section of pipe. The equation is V =.25 d2 l There d is the inside diameter of the pipe, and l is its length. You could key in the calculation over and over, for example,.25 2.calculates the volume of 16 inches of 1/2inch diameter pipe (78.5398 cubic inches). However, by storing the 2 equation, you get the HP 32SII to "remember" the relationship between diameter, length, and volumeso you can use it many times. Put the calculator in Equation mode and type in the equation using the following keystrokes:
Selects Equation mode, or the
or the current equation current shown by the EQN annunciator.
Begins a new equation, turning on the " " equationentry cursor. turns on the A.Z annunciator so you can enter a variable name. V.25 _ V types and moves the cursor to the right. Digit entry uses the "_" digitentry cursor.
ends the number and restores the " " cursor. _ types. scrolls o f the left side of the display. Terminates and displays the equation. and press direction. Shows the checksum and length for the equation, so you can check your keystrokes. above shows that part of the means you can equation doesn't fit in the display, to see characters in that
By comparing the checksum and length of your equation with those in the example, you can verify that you've entered the equation properly. (See "Verifying Equations" at the end of this chapter for more information.) Evaluate the equation (to calculate V):
Prompts for variables on the righthand side of the equation.
Prompts for D first; value is the current value of D.

2 value

Enters 2 1/2 inches as a fraction. Stores D, prompts for L; value is current value of L. Stores L; calculates V in cubic inches and stores the result in V.
Summary of Equation Operations
All equations you create are saved in the equation list. This list is visible whenever you activate Equation mode. You use certain keys to perform operations involving equations. They're described in more detail later.

ALOG RND ASIN ASINH HMS LB GAL
SQ ABS ACOS ACOSH %CHG C RANDOM ^
SQRT x! ATAN ATANH XROOT F
For convenience, prefixtype functions, which require one or two arguments, display a left parenthesis when you enter them. The prefix functions that require two arguments are %CHG, XROOT, Cn,r and Pn,r. Separate the two arguments with a space. In an equation, the XROOT function takes its arguments in the opposite order from RPN usage. For example, to is equivalent to. All other twoargument functions take their arguments in the Y, X order used for RPN. For example, 28 4{ } is equivalent to. For twoargument functions, be careful if the second argument is negative. The second argument must not start with "subtraction" ( ). For a number, use. For a variable, use parentheses and. These are valid equations:
Six of the equation functions have names that differ from their equivalent RPN operations:

RPN Operation

x2 ex 10x 1/x

Equation function

SQ EXP ALOG INV X ROOT ^
Example: Perimeter of a Trapezoid. The following equation calculates the perimeter of a trapezoid. This is how the equation might appear in a book: Perimeter = a + b + h (

+ ) sin sin

The following equation obeys the syntax rules for HP 32SII equations:
Parentheses used to group items
P=A+B+Hx(1SIN(T)+1SIN(F))
Single letter name No implied multiplication Division is done before addition
The next equation also obeys the syntax rules. This equation uses the inverse function, , instead of the fractional form,. Notice that the SIN function is "nested" inside the INV function. (INV is typed by.)
Example: Area of a Polygon. The equation for area of a regular polygon with n sides of length d is: Area =

1 cos( /n) ndsin(/n)

d 2 /n
You can specify this equation as
Notice how the operators and functions combine to give the desired equation. You can enter the equation into the equation list using the following keystrokes:

A N.25 N D 2 N

Linear regression and linear estimation ( x and
Weighted mean (x weighted by y).
A Summation statistics: n, x, y, x2, y2, and xy.

L.R. x,y s, SUMS

y x 2 y 2 xy
Entering Statistical Data
One and twovariable statistical data are entered (or deleted) in similar fashion using the (or ) key. Data values are accumulated as summation statistics in six statistic's registers (28 through 33), whose names and see. are displayed ire the SUMS menu. (Press Note
Always clear the statistics registers before entering a new set of statistical data (press {} ).
Entering OneVariable Data
1. Press {} to clear existing statistical data. 2. Key in each xvalue and press. 3. The display shows n, the number of statistical data values now accumulated. actually enters two variables into the statistics registers because Pressing the value already in the Yregister is accumulated as the yvalue. For this reason, the calculator will perform linear regression and show you values based on y even when you have entered only xdata or even if you have entered an unequal number of xand yvalues. No error occurs, but the results are obviously not meaningful. To recall a value to the display immediately after it has been entered, press.
Entering TwoVariable Data
When your data consist of two variables, x is the independent variable and y is the dependent variable. Remember to enter an (x, y) pair in reverse order (y x) so that y ends up in the Yregister and X in the Xregister. 1. 2. 3. 4. Press {} to clear existing statistical data. Key in the yvalue first and press. Key in the corresponding xvalue and press. 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 This deletes the value(s) and decrements n. 2. Enter the correct value(s) using. , press.
If the incorrect values were the ones just entered, press to retrieve them, then press to delete them. (The incorrect yvalue was still in the Yregister, and its Tvalue was saved in the LAST X register.) Example: Key in the x, yvalues on the left, these make the corrections shown on the right:

Initial x, y

Programming Techniques 1313
Example: Controlling the Fraction Display. The following program lets you exercise the calculator's fractiondisplay capability. The program prompts for and uses your inputs for a fractional number and a denominator (the /c value). The program also contains examples of how the three fractiondisplay flags (7, 8, and 9) and the "messagedisplay" flag (10) are used. Messages in this program are listed a MESSAGE and are entered as equations: 1. Set Equationentry mode by pressing (the EQN annunciator turns on). 2. Press letter for each alpha character in the message; press (the key) for each space character. 3. Press to insert the message in the current program line and end Equationentry mode.
Begins the fraction program. Clears three fraction flags.
Displays messages. Selects decimal base. Prompts for a number. Prompts for denominator (2 4095). Displays message, then shows the decimal number.
Sets /c value and sets flag 7. Displays message, then shows the fraction.
1314 Programming Techniques
Sets flag 8. Displays message, then shows the fraction.
Sets flag 9. Displays message, then shows the fraction.
Goes to beginning of program. Checksum and length: 10C3 102.0
Use the above program to see the different forms of fraction display:

F 2.53 16

value value
Executes label F; prompts for a fractional number (V). Stores 2.53 in V; prompts for denominator (D). Stores 16 as the /c value. Displays message, then the decimal number. Message indicates the fraction format (denominator is no greater than 16), then shows the fraction. indicates that the numerator is "a little below" 8. Message indicates the fraction
Programming Techniques 1315
format (denominator is factor of 16), then shows the fraction. Message indicates the fraction format (denominator is 16), then shows the fraction. Stops the program and clears flag
Branching backwards that is, to a label in a previous line makes it possible to execute part of a program more than once. This is called looping.
This routine (taken from the "Coordinate Transformations" program on page 1531 in chapter 15) is an example of an infinite loop. It is used to collect the initial data prior to the coordinate transformation. After entering the three values, it is up to the user to manually interrupt this loop by selecting the transformation to be performed (pressing N for the oldtonew system or O for the newtoold system).

Program Instructions:

1. Press { } to clear all programs and variables. This program requires all but 2 bytes of memory while running.
1528 Mathematics Programs

2. 3. 4. 5.

Key in the program routines; press when done. Press P to start the polynomial root finder. Key in F, the order of the polynomial, and press At each prompt, key in the coefficient and press. You're not prompted for the highestorder coefficient it's assumed to be 1. You must enter 0 for coefficients that are 0. Coefficient A must not be 0.

Terms mid Coefficients

Order xx4 E 1 x3 D D 1 x2 C C C 1 x B B B B Constant A A A A
6. After you enter the coefficients, the first root is calculated. A real root is displayed as real value. A complex root is displayed as real part, (Complex roots always occur in pairs of the for u i v, and are labeled in the output as real part and i =imaginary part, which you'll see in the next step.) 7. Press repeatedly to see the other roots, or to see i = imaginary part, the imaginary part of a complex root. The order of the polynomial is same as the number of roots you get. 8. For a new polynomial, go to step 3. A through E F G H X i Coefficients of tints of polynomial; scratch. Order of polynomial; scratch. Scratch. Pointer to polynomial coefficients. The value f a real root, or the real part of complex root The imaginary part of a complex root; also used as are index variable.
Mathematics Programs 1529
Exampl e 1: Find the roots of x5 x4 101x3 +101x2 + 100x 100 = 0.

P 100 100

value value value value value value
Starts the polynomial root finder; prompts for order. Stores 5 its F; prompts for E. Stores 1 in E; prompts for D. Store 101 in D. prompts for C. Stores 101 in C; prompts for B. Stores 100 in B; prompts for A. Stores 100 in A; calculates the first root. Calculates the second root. Displays the third root. Displays the fourth root. Displays the fifth root.
Example 2: Find the roots of 4x4 8x3 13x2 10x + 22 = 0. Because the coefficient of the highestorder term must be 1, divide that coefficient into each of the other coefficients.
Starts the polynomial root finder; prompts for order. Stores 4 its F; prompts for D. Stores 8/4 in D; prompts for C. Store 13/4 in C. prompts for B.
1530 Mathematics Programs
Stores 10/4 in B; prompts for A. Stores 22/4 in A; calculates the first root. Calculates the second root. Displays the real part of the third root. Displays the imaginary part of the third root. Displays the real part of the fourth root. Displays the imaginary part of the fourth root.

Statistics Programs 1619

Flags Used: None. Memory Required: 143 bytes: 71 for programs, 72 for data.
Program Instructions: 1. 2. 3. 4. 5. 6. Key in the program routines; press when done. Press S to start entering new data. Key in xivalue (data point) and press. Key in f ivalue (frequency) and press. Press after VIEWing the number of points entered. Repeat steps 3 through 5 for each data point.
If you discover that you have made a data-entry error ( xi or fi ) after you have pressed in step 4, press U and then press again. Then go back to step 3 to enter the correct data. G to calculate and 7. When the last data pair has been input, press display the grouped standard deviation. 8. Press to display the weighted mean of the grouped data. 9. To add additional data points, press and continue at step 3. To start a new problem, start at step 2.
Variables Used: X F N S M Data point. Datapoint frequency. Datapair counter. Grouped standard deviation. Weighted mean.

1620 Statistics Programs

i Register 28 Register 29 Register 31
Index variable used to indirectly address the correct statistics register. Summation fi. Summation xifi. Summation xi2fi.
Exampl e: Enter the following data and calculate the grouped standard deviation. Group xi fi 37 115

S 5 17

Prompts for the first xi. Stores 5 in X; prompts for first fi. Stores 17 in F; displays the counter. Prompts for the second xi.
Prompts for second fi. Displays the counter. Prompts for the third xi. Prompts for the third fi. Displays the counter.
You erred by entering 14 instead of 13 for x3. Undo your error by executing routine U: U Removes the erroneous data; displays the revised counter. Prompts for new third xi. 13 Prompts for the new third fi.

Statistics Programs 1621

Displays the counter. Prompts for the fourth x i.
Prompts for the fourth fi. Displays the counter. Prompts for the fifth x1. Prompts for the fifth fi. Displays the counter. Prompts for the sixth xi. Prompts for the sixth fi. Displays the counter. Calculates and displays the grouped standard deviation (sx) of the six data points. Calculates and displays weighted mean ( x ). Clears VIEW.

gamma function, 4-12 go to. See GTO grads (angle units), 4-3, A-2 Grandma Hinkle, 11-7 grouped standard deviation, 16-19 finds PRGM TOP, 12-6, 12-21, 13-5 finds program labels, 12-10, 12-21, 13-5 finds program lines, 12-20, 12-21, 13-5 GTO, 13-4, 13-16 guesses (for SOLVE), 7-2, 7-6, 7-7, 7-10, 14-5
help about calculator, A-1 hexadecimal numbers. See hex

Index6

numbers HEX annunciator, 10-1 hex numbers. See numbers arithmetic, 10-3 converting to, 10-1 range of, 10-6 typing, 10-1 Horner's method, 12-26 humidity limits for calculator, A-2 hyperbolic functions, 4-6
i, 3-8, 13-19 (i), 3-8, 13-19, 13-20, 13-24 imaginary part (complex numbers), 9-1, 9-2 indirect addressing, 13-19, 13-20, 13-21 INPUT always prompts, 13-10 entering program data, 12-12 in integration programs, 14-8 in SOLVE programs, 14-2 responding to, 12-14 showing hidden digits, 12-14 integer-part function, 4-15 integration accuracy, 8-2, 8-6, 8-7, D-2 base mode,.12-25, 14-10 difficult functions, D-2, D-7 display format, 8-2, 8-6, 8-8 evaluating programs, 14-7 how it works, D-1 in programs, 14-9 interrupting, B-3
limits of, 8-2, 14-7, D-7 memory usage, 8-2, 12-22, B-2, B-3 purpose, 8-1 restrictions, 14-10 results on stack, 8-2, 8-7 resuming, 14-7 stopping, 8-2, 14-7 subintervals, D-7, D-9 time required, 8-6, D-7 transforming variables, D-9 uncertainty of result, 8-2, 8-6, 8-7, D-2 using, 8-2 variable of, 8-2 intercept (curve-fit), 11-8, 16-1 interest (finance), 17-3 intermediate results, 2-13 inverse function, 1-14, 9-3 inverse hyperbolic functions, 4-6. inverse-normal distribution, 16-12 inverse trigonometric functions, 4-4 ISG, 13-16
keys alpha, 1-2 letters, 1-2 shifted, 1-2 top-row actions, 6-8, 12-7
LASTx function, 2-9 LAST X register, 2-9, B-8

Index7

lender (finance), 17-1 length conversions, 4-12 letter keys, 1-2 limits of integration, 8-2, 14-7 linear regression (estimation), 11-8, 16-1 linear-regression menu, 11-8 logarithmic curve fitting, 16-1 logarithmic functions, 4-2, 9-3 loop counter, 13-16, 13-17, 13-21 looping, 13-15, 13-16

ukasiewicz, 2-1

variable catalog, 1-21, 3-4 memory amount available, 1-21, B-2 clearing, 1-4, 1-22, A-1, A-4, B-1, 11-4 clearing equations, 6-10 clearing programs, 1-22, 12-6, 12-23 clearing statistics registers, 11-2, 11-13 clearing variables, 1-22, 3-5 contents, 1-21 deallocating, B-3 equations, B-2 full, A-1 integration usage, 8-2 maintained while off, 1-1 programs, 12-21, 12-22, B-3 size, 1-21, B-1 stack, 2-1 statistics registers, 11-13 usage, 12-22, B-1, B-2 variables, 3-5 MEMORY CLEAR, A-4, B-4, E-3 MEMORY FULL, B-1, E-3 menu keys, 1-5 menus example of using, 1-7 general operation, 1-5 leaving, 1-3, 1-8 list of, 1-6 messages clearing, 1-3, 1-21 displaying, 12-15, 12-18 in equations, 12-15 responding to, 1-21, E-1 summary of, E-1
mantissa, 1-12, 1-18 mass conversions, 4-12 math complex-number, 9-1, 9-4 general procedure, 1-14 intermediate results, 2-13 long calculations, 2-13 order of calculation, 2-16 real-number, 4-1 stack operation, 2-5, 9-2 matrix inversion, 15-13 maximum of function, C-9 mean menu, 11-4 means (statistics) calculating, 11-4 normal distribution, 16-12 program catalog, 1-21, 12-22 reviews memory, 1-21

Index8

minimum of function, C-9 modes. See angular mode, base mode, Equation mode, Fraction-display mode, Program-entry mode MODES menu angular mode, 4-4 setting radix, 1-1.6 money (finance), 17-1
negative numbers, 1-11, 9-3, 10-5 nested routines, 13-3, 14-10 normal distribution, 16-12 numbers. See binary numbers, hex numbers, octal numbers, variables bases, 10-1, 12-25 changing sign of, 1-11, 1-14, 9-3 clearing, 1-3, 1-4, 1-11, 1-13 complex, 9-1 decimal places, 1-16 display format, 1-16, 10-5 doing arithmetic, 1-14 editing, 1-3, 1-11, 1-13 E in, 1-11, 1-12, A-1 exchanging, 2-4 finding parts of, 4-15 fractions in, 1-19, 5-1 in equations, 6-0i in programs, 12-6 internal representation, 1-16, 10-5 large and small, 1-11, 1-13 limitations, 1-11 mantissa, 1-12 memory usage, 12-22, B-2
negative, 1-11, 9-3, 10-5 order in calculations, 1-15 periods and commas in, 1-16, A-1 precision, 1-16, C-16 prime, 17-7 range of, 1-13, 10-6 real, 4-1, 8-1 recalling, 3-2 reusing, 2-6, 2-11 rounding, 4-15 showing all digits, 1-18, 10-8 storing, 3-2 truncating, 10-5 typing, 1-11, 1-12, 10-1
octal numbers. See numbers arithmetic, 10-3 converting to, 10-1 range of, 10-6 typing, 10-1 OCT annunciator, 10-1 , 1-1 one-variable statistics, 11-2 overflow flags, 13-9, E-4 result of calculation, 1-13, 10-3, 10-6 setting response, 13-9, E-4 testing occurrence, 13-9

, 4-3, A-2

parentheses in arithmetic, 2-13

Index9

in equations, 6-6, 6-7, 6-16 memory usage, 12-22 PARTS menu, 4-15 pause. See PSE payment (finance), 17-1 percentage functions, 4-6 periods (in numbers), 1-16, A-1 permutations, 4-13 polar-to-rectangular coordinate conversion, 4-8, 9-6, 15-1 poles of functions, C-6 polynomials, 12-26, 15-22 population standard deviations, 11-7 power annunciator, 1-1, A-2 power curve fitting, 16-1 power functions, 1-12, 4-2, 9-4 precedence (equation operators), 6-16 precision (numbers), 1-16, 1-18, C-16 present value, See financial calculations PRGM TOP, 12-4, 12-6, 12-21, E-4 prime number generator, 17-7 probability functions, 4-12 normal distribution, 16-12 PROB menu, 4-13 program catalog, 1-21, 12-22 Program-entry mode, 1-3, 12-6 program labels branching to, 13-2, 13-4, 13-15 checksums, 12-23

C. ALG: Summary...C-1

About ALG.... C-1 Doing Two argument Arithmetic in ALG.. C-2 Simple Arithmetic... C-2 Power Functions... C-3 Percentage Calculations.. C-3 Permutations and Combinations.. C-4 Quotient and Remainder Of Division. C-4 Parentheses Calculations.. C-4 Exponential and Logarithmic Functions.. C-5 Trigonometric Functions... C-6 Hyperbolic functions... C-6 Parts of numbers... C-7 Reviewing the Stack... C-7 Integrating an Equation.. C-8 Operations with Complex Numbers.. C-8 Arithmetic in Bases 2, 8, and 16.. C-10 Entering Statistical TwoVariable Data.. C-11
D. More about Solving.. D-1
How SOLVE Finds a Root.. D-1 Interpreting Results.. D-3 When SOLVE Cannot Find a Root.. D-8 RoundOff Error... D-13
E. More about Integration.. E-1
How the Integral Is Evaluated.. E-1 Conditions That Could Cause Incorrect Results.. E-2 Conditions That Prolong Calculation Time.. E-7
F. Messages... F-1 G. Operation Index.. G-1

Part 1

Basic Operation

Getting Started

performed differently in ALG mode. Appendix C explains how to use your calculator in ALG mode.
Watch for this symbol in the margin. It identifies examples or keystrokes that are shown in RPN mode and must be

Important Preliminaries

Turning the Calculator On and Off
To turn the calculator on, press To turn the calculator off, press
. ON is printed on the bottom of the key. That is, press and release the shift
key, then press (which has OFF printed in yellow above it). Since the calculator has Continuous Memory, turning it off does not affect any information you've stored. To conserve energy, the calculator turns itself off after 10 minutes of inactivity. If you see the lowpower indicator (
) in the display, replace the batteries as soon as
possible. See appendix A for instructions.
Adjusting Display Contrast
Display contrast depends on lighting, viewing angle, and the contrast setting. To increase or decrease the contrast, hold down the key and press
Highlights of the Keyboard and Display

Shifted Keys

Each key has three functions: one printed on its face, a leftshifted function (yellow), and a rightshifted function (blue). The shifted function names are printed in yellow above and in blue on the bottom of each key. Press the appropriate shift
) before pressing the key for the desired function. For example, to turn the calculator off, press and release the shift key, then press.

key ( or

Twentyfour people grouped six at a time. Total number of combinations possible.
If employees are chosen at random, what is the probability that the committee will contain six women? To find the probability of an event, divide the number of combinations for that event by the total number of combinations.
Fourteen women grouped six at a time. Number of combinations of six women on the committee. Brings total number of combinations back into the X register. Divides combinations of women by total combinations to find probability that any one combination would have all women.

Parts of Numbers

These functions are primarily used in programming.

Integer part

To remove the fractional part of x and replace it with zeros, press (). (For example, the integer part of 14.2300 is 14.0000.)

Fractional part

To remove the integer part of x and replace it with zeros, press (). (For example, the fractional part of 14.2300 is 0.2300)

Absolute value

To replace a number in the x-register with its absolute value, press complex numbers and vectors, the absolute value of: 1. 2. 3. a complex number in ra format is r a complex number in xiy format is a vector [A1,A2,A3, An] is

x2 + y2

A = A+ A+ + An 2
Argument value To extract the argument of a complex number, use complex number: 1. 2. in ra format is a in xiy format is Atan(y/x)

=. The argument of a

Sign value To indicate the sign of x, press
(). If the x value is negative,
1.0000 is displayed; if zero, 0.0000 is displayed; if positive, 1.0000 is displayed.
Greatest integer To obtain the greatest integer equal to or less than given number, press
Example: This example summarizes many of the operations that extract parts of numbers.

To calculate:

The integer part of 2.47
() The fractional part of 2.47 () The absolute value of 7 The sign value of 9 () The greatest integer equal to

or less than 5.3 ()

The RND function ( ) rounds x internally to the number of digits specified by the display format. (The internal number is represented by 12 digits.) Refer to chapter 5 for the behavior of RND in Fractiondisplay mode.
In Chapter 1, the section Fractions introduced the basics of entering, displaying, and calculating with fractions. This chapter gives more information on these topics. Here is a short review of entering and displaying fractions: To enter a fraction, press twice: once after the integer part of a mixed number and again between the numerator and denominator of the fractional part of the number. To enter 2 3/8, press. To enter 5/8, press either or. To toggle Fraction-display mode on and off, press. When Fraction-display mode is turned off, the display reverts to the previous display format set via the Display menu. Choosing another format via this menu also turns off Fraction-display mode, if active. Functions work the same with fractions as they do with decimal numbers except for RND, which is discussed later in this chapter. The examples in this chapter all utilize RPN mode unless otherwise noted.

Type of Equation

Equality: g(x) = f(x) Example: x2 + y2 = r2 Assignment: y = f(x) Example: A = 0.5 b x h Expression: f(x) Example: x3 + 1

Result for

g(x) f(x) x2 + y2 r2 f(x) 0.5 b h f(x) x3 + 1 y f(x) A 0.5 b h
Also stores the result in the lefthand variable, A for example.
To evaluate an equation: 1. Display the desired equation. (See "Displaying and Selecting Equations" above.)
or. The equation prompts for a value for each variable
needed. (If the base of a number in the equation is different from the current base, the calculator automatically changes the result to the current base.) 3. For each prompt, enter the desired value: If the displayed value is good, press
If you want a different value, type the value and press. (Also see "Responding to Equation Prompts" later in this chapter.) To halt a calculation, press or. The message is shown in line 2. The evaluation of an equation takes no values from the stack it uses only numbers in the equation and variable values. The value of the equation is returned to the X register.
Using ENTER for Evaluation
If an equation is displayed in the equation list, you can press ends the equation it doesn't evaluate it.)
to evaluate the equation. (If you're in the process of typing the equation, pressing only
If the equation is an assignment, only the righthand side is evaluated. The result is returned to the Xregister and stored in the lefthand variable, then the variable is viewed in the display. Essentially, finds the value of the lefthand variable. If the equation is an equality or expression, the entire equation is evaluated just as it is for. The result is returned to the Xregister. Example: Evaluating an Equation with ENTER. Use the equation from the beginning of this chapter to find the volume of a 35mm diameter pipe that's 20 meters long.
Displays the desired equation. Starts evaluating the assignment equation so the value will be stored in V. Prompts for variables on the righthand side of the equation. The current value for D is 2.5. Stores D, prompts for L, whose current value is 16. Stores L in millimeters; calculates V in cubic millimeters, stores the result in V, and displays V. Changes cubic millimelers to liters (but doesn't change V.

( as required)

Using XEQ for Evaluation
If an equation is displayed in the equation list, you can press

to evaluate the

equation. The entire equation is evaluated, regardless of the type of equation. The result is returned to the Xregister.
Example: Evaluating an Equation with XEQ. Use the results from the previous example to find out how much the volume of the pipe changes if the diameter is changed to 35.5 millimeters.
Displays the desired equation. Starts evaluating the equation to find its value. Prompts for all variables. Keeps the same V, prompts for D. Stores new D, Prompts for L. Keeps the same L; calculates the value of the equation the imbalance between the left and right sides. Changes cubic millimeters to liters.

Understanding and Controlling SOLVE
SOLVE first attempts to solve the equation directly for the unknown variable. If the attempt fails, SOLVE changes to an iterative (repetitive) procedure. The procedure starts by evaluating the equation using two initial guesses for the unknown variable. Based on the results with those two guesses, SOLVE generates another, better guess. Through successive iterations, SOLVE finds a value for the unknown that makes the value of the equation equal to zero. When SOLVE evaluates an equation, it does it the same way

does any

"=" in the equation is treated as a " ". For example, the Ideal Gas Law equation is evaluated as P V (N R T). This ensures that an equality or assignment equation balances at the root, and that an expression equation equals zero at the root. Some equations are more difficult to solve than others. In some cases, you need to enter initial guesses in order to find a solution. (See "Choosing Initial Guesses for SOLVE," below.) If SOLVE is unable to find a solution, the calculator displays . See appendix D for more information about how SOLVE works.

Verifying the Result

After the SOLVE calculation ends, you can verify that the result is indeed a solution of the equation by reviewing the values left in the stack: The Xregister (press to clear the viewed variable) contains the solution (root) for the unknown; that is, the value that makes the evaluation of the equation equal to zero.
The Yregister (press ) contains the previous estimate for the root or equals to zero. This number should be the same as the value in the Xregister. If it is not, then the root returned was only an approximation, and the values in the X and Yregisters bracket the root. These bracketing numbers should be close together. The Z register (press again) contains D-value of the equation at the root. For an exact root, this should be zero. If it is not zero, the root given was only an approximation; this number should be close to zero. If a calculation ends with the , the calculator could not converge on a root. (You can see the value in the Xregister the final estimate of the root by pressing
or to clear the message.) The values in the X and Yregisters
bracket the interval that was last searched to find the root. The Zregister contains the value of the equation at the final estimate of the root. If the X and Yregister values aren't close together, or the Zregister value isn't close to zero, the estimate from the Xregister probably isn't a root. If the X and Yregister values are close together, and the Zregister value is close to zero, the estimate from the Xregister may be an approximation to a root.
Interrupting a SOLVE Calculation

or , and the message will be shown. The current best estimate of the root is in the unknown variable; use to view it without disturbing the stack, but solving cannot be resumed.
To halt a calculation, press
Choosing Initial Guesses for SOLVE
The two initial guesses come from: The number currently stored in the unknown variable. The number in the Xregister (the display).
These sources are used for guesses whether you enter guesses or not. If you enter only one guess and store it in the variable, the second guess will be the same value since the display also holds the number you just stored in the variable. (If such is the case, the calculator changes one guess slightly so that it has two different guesses.) Entering your own guesses has the following advantages: By narrowing the range of search, guesses can reduce the time to find a solution. If there is more than one mathematical solution, guesses can direct the SOLVE procedure to the desired answer or range of answers. For example, the equation of linear motion d = v0 t + 1/2 gt 2 can have two solutions for t. You can direct the answer to the required solution by entering appropriate guesses. The example using this equation earlier in this chapter didn't require you to enter guesses before solving for T because in the first part of that example you stored a value for T and solved for D. The value that was left in T was a good (realistic) one, so it was used as a guess when solving for T. If an equation does not allow certain values for the unknown, guesses can prevent these values from occurring. For example, y = t + log x results in an error if x 0 (message ). In the following example, the equation has more than one root, but guesses help find the desired root.
Example: Using Guesses to Find a Root. Using a rectangular piece of sheet metal 40 cm by 80 cm, form an opentop box having a volume of 7500 cm3. You need to find the height of the box (that is, the amount to be folded up along each of the four sides) that gives the specified volume. A taller box is preferred to a shorter one.

H H 80 _ 2 H 80 H

If H is the height, then the length of the box is (80 2H) and the width is (40 2H). The volume V is: V = ( 80 2H ) (40 2H ) H which you can simplify and enter as V= ( 40 H ) ( 20 H ) 4 H Type in the equation:
Selects Equation mode and starts the equation

4 H H

_ _ Terminates and displays the equation. Checksum and length.

This uncertainty indicates that the result might be correct to only three decimal places. In reality, this result is accurate to seven decimal places when compared with the actual value of this integral. Since the uncertainty of a result is calculated conservatively, the calculator's approximation in most cases is more accurate than its uncertainty indicates.
This chapter gives you instructions for using integration in the HP 35s over a wide range of applications. Appendix E contains more detailed information about how the algorithm for integration works, conditions that could cause incorrect results and conditions that prolong calculation time, and obtaining the current approximation to an integral.
Operations with Complex Numbers
The HP 35s can use complex numbers in the form
It has operations for complex arithmetic (+, , , ), complex trigonometry (sin, cos, tan), and the mathematics functions z, 1/z, are complex numbers). The form, x+yi, is only available in ALG mode. To enter a complex number: Form: 1. Type the real part. 2. Press6. 3. Type the imaginary part. Form: 1. Type the real part. 2. Press 3. Type the imaginary part. 4. Press6. Form: 1. Type the value of r. 2. Press?. 3. Type the value of. The examples in this chapter all utilize RPN mode unless otherwise noted.
z1z 2 , ln z, and e z. (where z1 and z2

The Complex Stack

A complex number occupies part 1 and part 2 of a stack level. In RPN mode, the complex number occupying part 1 and part 2 of the X-register is displayed in line 2, while the complex number occupying part 1 and part 2 of the Y-register is displayed in line 1.
Part3 T Part2 Part1 Part3 Z Part2 Part1 Part3 Y
Y1 or a1 X1 or r1 Pa r t 3
X1iY1 (Display in line 1) or r1 a1

Y2 or a2 X2 or r2

(Display in line 2)
or r2 a2 Complex Result,Z

Complex Stack

Complex Operations
Use the complex operations as you do real operations in ALG and RPN mode. To do an operation with one complex number: 1. Enter the complex number z as described before.
2. Select the complex function.
Functions for One Complex Number, z To Calculate:
Change sign, z Inverse, 1/z Natural log, ln z Natural antilog, ez Sin z Cos z Tan z Absolute value, ABS(z) Argument value, ARG(z)
To do an arithmetic operation with two complex numbers: 1. Enter the first complex number, z1 as described before.

() to recall the sum of the xvalues. () to recall the sum of the yvalues.
(), (), and () to recall the sums of the squares and the sum of
the products of the x and y values that are of interest when performing other statistical calculations in addition to those provided by the calculator. If you've entered statistical data, you can see the contents of the statistics registers. Press
(), then use and to view the statistics
registers. Example: Viewing the Statistics Registers. Use
to store data pairs (1,2) and (3,4) in the statistics registers. Then view the
stored statistical values.
Clears the statistics registers. Stores the first data pair (1,2). Stores the second data pair (3,4).

() ()

Displays VAR catalog and views n register. views xy register.
Statistical Operations 12-11
Views y2 register. Views x2 register. Views y register. Views x register. Views n register. Leaves VAR catalog.
Access to the Statistics Registers
The statistics register assignments in the HP 35s are shown in the following table. Summation registers should be referred to by names and not by numbers in expression, equations and programs.
Statistics Registers Register

n x y x2 y2 xy

Number

-27 -28 -29 -30 -31 -32

Number of accumulated data pairs. Sum of accumulated xvalues. Sum of accumulated yvalues. Sum of squares of accumulated xvalues. Sum of squares of accumulated yvalues. Sum of products of accumulated x and y values.
12-12 Statistical Operations
You can load a statistics register with a summation by storing the number (-27 through -32) of the register you want in I or J and then storing the summation (value
7 or A). Similarly, you can press 7 or A (or 7 or A ) to view (or recall)a register value the display is labeled with
the register name. The SUMS menu contains functions for recalling the register values. See "Indirectly Addressing Variables and Labels" in chapter 14 for more information.
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

Flag Status Clear

(Default)

FractionControl Flags 7

Fraction display off; display real numbers in the current display format. Fraction display on; display real numbers as fractions.
Fraction denominators not greater than the /c value. Fraction denominators are factors of the /c Value.
Reduce fractions to smallest form.
No reduction of fractions. (Used only if flag 8 is set.)
14-10 Programming Techniques
Flag 10 controls program execution of equations: When flag 10 is clear (the default state), equations in running programs are evaluated and the result put on the stack. When flag 10 is set, equations in running programs are displayed as messages, causing them to behave like a VIEW statement: 1. Program execution halts. 2. The program pointer moves to the next program line. 3. The equation is displayed without affecting the stack. You can clear the display by pressing key's function. 4. If the next program line is a PSE instruction, execution continues after a 1second pause. The status of flag 10 is controlled only by execution of the SF and CF operations from the keyboard, or by SF and CF statements in programs. Flag 11 controls prompting when executing equations in a program it doesn't affect automatic prompting during keyboard execution: When flag 11 is clear (the default state), evaluation, SOLVE, and FN of equations in programs proceed without interruption. The current value of each variable in the equation is automatically recalled each time the variable is encountered. INPUT prompting is not affected. When flag 11 is set, each variable is prompted for when it is first encountered in the equation. A prompt for a variable occurs only once, regardless of the number of times the variable appears in the equation. When solving, no prompt occurs for the unknown; when integrating, no prompt occurs for the variable of integration. Prompts halt execution. Pressing resumes the calculation using the value for the variable you keyed in, or the displayed (current) value of the variable if is your sole response to the prompt. Flag 11 is automatically cleared after evaluation, SOLVE, or FN of an equation in a program. The status of flag 11 is also controlled by execution of the SF and CF operations from the keyboard, or by SF and CF statements in programs.
or. Pressing any other key executes that

[x (x + 0.3)] 0.5 = 0

Enter the equation as an expression:

X4 X

First attempt to find a positive root:
Your positive guesses for the root. Selects Equation mode; displays the left end of the equation. Calculates the root using guesses 0 and 10.
Now attempt to find a negative root by entering guesses 0 and 10. Notice that the function is undefined for values of x between 0 and 0.3 since those values produce a positive denominator but a negative numerator, causing a negative square root.
Selects Equation mode; displays the left end of the equation. No root found for f(x).
Example: A Local "Flat" Region. Find the root of the function f(x) = x + 2 if x < 1, f(x) = 1 for 1 x 1 (a local flat region), f(x) = x + 2 if x >1. In RPN mode, enter the function as the program:
Checksum and length: 9412 39
Solve for X using initial guesses of 108 and 108.

Enters guesses.

X J X
_ Selects program "J" as the function. Solves for X; displays the result.

RoundOff Error

The limited (12digit) precision of the calculator can cause errors due to rounding off, which adversely affect the iterative solutions of SOLVE and integration. For example,
[( x + 1) + 1015 ]2 - 1030 = 0
has no roots because f(x) is always greater than zero. However, given initial guesses of 1 and 2, SOLVE returns the answer 1.0000 due to roundoff error. Roundoff error can also cause SOLVE to fail to find a root. The equation

x2 - 7 = 0

has a root at
7. However, no 12digit number exactly equals

7 , so the

calculator can never make the function equal to zero. Furthermore, the function never changes sign SOLVE returns the message .

More about Integration

This appendix provides information about integration beyond that given in chapter 8.
How the Integral Is Evaluated
The algorithm used by the integration operation, , calculates the integral of a function f(x) by computing a weighted average of the function's values at many values of x (known as sample points) within the interval of integration. The accuracy of the result of any such sampling process depends on the number of sample points considered: generally, the more sample points, the greater the accuracy. If f(x) could be evaluated at an infinite number of sample points, the algorithm could neglecting the limitation imposed by the inaccuracy in the calculated function f(x) always provide an exact answer. Evaluating the function at an infinite number of sample points would take forever. However, this is not necessary since the maximum accuracy of the calculated integral is limited by the accuracy of the calculated function values. Using only a finite number of sample points, the algorithm can calculate an integral that is as accurate as is justified considering the inherent uncertainty in f(x). The integration algorithm at first considers only a few sample points, yielding relatively inaccurate approximations. If these approximations are not yet as accurate as the accuracy of f(x) would permit, the algorithm is iterated (repeated) with a larger number of sample points. These iterations continue, using about twice as many sample points each time, until the resulting approximation is as accurate as is justified considering the inherent uncertainty in f(x).

Attempted an operation with an invalid indirect value ((I) is not defined). Attempted an operation with an invalid indirect value ((J) is not defined). Attempted to take a logarithm of zero or (0 + i0). Attempted to take a logarithm of a negative number. All of user memory has been erased (see page ). The calculator has insufficient memory available to do the operation (See appendix B). The condition checked by a test instruction is not true. (Occurs only when executed from the keyboard.) Attempted to refer to a nonexistent program label (or line number) with ,, or. Note that the error can mean you explicitly (from the keyboard) called a program label that does not exist; or the program that you called referred to another label, which does not exist. The result of integration does not exist.
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.

or or

118 63

, 1/x 10x % %CHG + x

Separates the two or three arguments of a function.
Reciprocal. Common exponential.
Returns 10 raised to the power.

Percent.

Returns (y x) 100.

Percent change.

Returns (x y)(100 y).
Returns the approximation
3.14159265359 (12 digits).
Accumulates (y, x) into statistics

registers.

Removes (y, x) from statistics registers. () Returns the sum of xvalues.

1211 1

Returns the sum of squares of x values.
() Returns the sum of products of xand yvalues.
() Returns the sum of yvalues. ()
Returns the sum of squares of y values.

1211 1211

Returns population standard deviation of xvalues:

x )2 n

Returns population standard deviation of yvalues:

FN d variable

y )2 n

82 157

( _) variable Integrates the displayed equation or the program selected by FN=, using lower limit of the variable of integration in the Yregister and upper limit of the variable of integration in the Xregister. 4parenthesis. press to leave
the parenthesis for further calculation.

3: A vector symbol for

performing vector operations

101 91

?: A complex number symbol for performing complex number operations

A through Z ABS

variable Value of named

variable.

Absolute value. Returns x. Arc cosine.

Returns cos 1x.

ACOS ACOSH
Hyperbolic arc cosine. Returns cosh 1 x.
Activates Algebraic mode.

Common exponential.

Returns 10 raised to the specified power (antilogarithm).
Displays all significant digits. May have to scroll right () to see all of the digits.

AND ARG

>(1AND)

Logic operator

114 417
Replaces a complex number with its Argument

() Returns the

correlation coefficient between the x and yvalues:
(x x )(y y ) (x x ) (y y )

i i 2 i i

Changes the display of complex numbers.

RAD RAD RADIX ,

9 () Selects Radians angular mode. Degrees to radians. Returns (2/360) x. 8 (6)
Selects the comma as the radix mark (decimal point).

RADIX.

8 () Selects the period as the radix mark (decimal point). Executes the RANDOM
function. Returns a random number in the range 0 through 1.

RANDOM

RCL variable
Recall. Copies variable into the Xregister.

Operation Index G-11

RCL+ variable RCL variable RCLx variable RCL variable RMDR

Returns x + variable.

variable.

Returns x variable.

() Produces the remainder of a division operation involving two integers. Round.
Rounds x to n decimal places in FIX n display mode; to n + 1 significant digits in SCI n or ENG n display mode; or to decimal number closest to displayed fraction in Fraction display mode.

418 58

9()Activates Reverse

Polish notation.

Return.
Marks the end of a program; the program pointer returns to the top or to the calling routine.

Roll down.

Moves t to the Zregister, z to the Y register, y to the Xregister, and x to the Tregister in RPN mode. Displays the X,Y,Z,T menu to review the stack in ALG mode.

Roll up.

Moves t to the Xregister, z to the T register, y to the Zregister, and x to the Yregister in RPN mode. Displays the X,Y,Z,T menu to review the stack in ALG mode.
Displays the standarddeviation Menu.
8() n Selects Scientific display with n decimal places. (n = 0 through 11.) Restarts the random
number sequence with the seed

415. 1

SF n SGN
Sets flag n (n = 0 through 11).

() Indicates the

sign of x. Shows the full mantissa (all 12 digits) of x (or the number in the current program line); displays hex checksum and decimal byte length for equations and programs.

SIN SINH

Sine.

Returns sin x.

71 151

Hyperbolic sine.

Returns sinh x.

SOLVE variable

Solves the displayed equation or the program selected by FN=, using initial estimates in variable and x.
SQ SQRT STO variable STO + variable STO variable STO variable STO variable
Inserts a blank space character during equation entry.
Square of argument. Square root of x. variable

Index-5

logarithmic functions 4-1, 9-3, C-5 logic AND 11-4 NAND 11-4 NOR 11-4 NOT 11-4 OR 11-4 XOR 11-4 loop counter 14-18, 14-23 looping 14-16, 14-17 ukasiewicz 2-1
program catalog 1-28, 13-22 reviews memory 1-28 variable catalog 1-28 mantissa 1-25 mass conversions 4-14 math complex-number 9-1 general procedure 1-18 intermediate results 2-12 long calculations 2-12 order of calculation 2-14 real-number 4-1 stack operation 2-5, 9-2 maximum of function D-8 mean menu 12-4 means (statistics) calculating 12-4 normal distribution 16-11 memory amount available 1-28 clearing 1-5, 1-29, A-1, A-4, B-1, B-3 clearing equations 6-9 clearing programs 1-28, 13-6, 1322 clearing statistics registers 12-2 clearing variables 1-28 full A-1 maintained while off 1-1 programs 13-21, B-2 size 1-28, B-1 stack 2-1
usage B-1 MEMORY CLEAR A-4, B-3, F-3 MEMORY FULL B-1, F-3 menu keys 1-6 menus example of using 1-8 general operation 1-6 leaving 1-4, 1-8 list of 1-6 messages clearing 1-4 displaying 13-16, 13-18 in equations 13-16 responding to 1-27, F-1 summary of F-1 minimum of function D-8 modes. See angular mode, base mode, Equation mode, Fraction-display mode, Program-entry mode MODES menu angular mode 4-4 money (finance) 17-1 multiplication, dividision 10-2
negative numbers 1-15, 9-3, 11-6 nested routines 14-2, 15-11 normal distribution 16-11 numbers. See binary numbers, hex numbers, octal numbers, variables bases 10-1, 13-25 changing sign of 1-15, 9-3 clearing 1-4, 1-5, 1-17 complex 9-1 display format 1-21, 11-6 E in 1-15, A-1 editing 1-4, 1-17 exchanging 2-4 finding parts of 4-17 fractions in 1-26, 5-1 in equations 6-5 in programs 13-7 internal representation 11-6 large and small 1-15, 1-17 negative 1-15, 9-3, 11-6 performing arithmetic calculations

Index-6

1-18 periods and commas in 1-23, A-1 precision D-13 prime 17-7 range of 1-17, 11-7 real 4-1 recalling 3-2 reusing 2-6, 2-10 rounding 4-18 showing all digits 1-25 storing 3-2 truncating 11-6 typing 1-15, 1-16, 11-1
1-1 OCT annunciator 11-1, 11-4 octal numbers. See numbers arithmetic 11-4 converting to 11-2 range of 11-7 typing 11-1 one-variable statistics 12-2 overflow flags 14-9, F-4 result of calculation 1-17, 11-5 setting response 14-9, F-4 testing occurrence 14-9
A-2 parentheses in arithmetic 2-12 in equations 6-5, 6-6, 6-15 pause. See PSE payment (finance) 17-1 percentage functions 4-6 periods (in numbers) 1-23, A-1 permutations 4-15 Physics constants 4-8 polar-to-rectangular coordinate conversion 4-10, 9-5 poles of functions D-6 polynomials 13-26 population standard deviations 12-7 power annunciator 1-1, A-3
power curve fitting 16-1 power functions 1-17, 4-2, 9-3 precedence (equation operators) 6-14 precision (numbers) 1-25, D-13 present value. See financial calculations PRGM TOP 13-4, 13-7, 13-21, F-4 prime number generator 17-7 probability functions 4-15 normal distribution 16-11 program catalog 1-28, 13-22 program labels branching to 14-2, 14-4, 14-16 checksums 13-23 clearing 13-6 duplicate 13-6 entering 13-4, 13-6 executing 13-10 indirect addressing 14-20, 14-21, 14-23 moving to 13-22 purpose 13-4 typing name 1-3 viewing 13-22 program lines. See programs program names. See program labels program pointer 13-6, 13-11, 13-19, 13-21, B-4 Program-entry mode 1-4, 13-6 programs. See program labels ALG operations 13-4 base mode 13-25 branching 14-2, 14-4, 14-6, 1416 calculations in 13-13 calling routines 14-1, 14-2 catalog of 1-28, 13-22 checksums 13-22, 13-23, B-2 clearing 13-6, 13-22, 13-23 clearing all 13-6, 13-23 comparison tests 14-7 conditional tests 14-7, 14-9, 1412, 14-17, 15-6 data input 13-5, 13-13, 13-14 data output 13-5, 13-14, 13-18