HP HP-15C - Manual

10 Contents Appendix A: Error Conditions .................................... 205 Appendix B: Stack Lift and the LAST X Register ............... 209 Digit Entry Termination .................................................... 209 Stack Lift ..............................................................

12 The HP-15C: A Problem Solver The HP-15C Advanced Programmable Scientific Calculator is a powerful problem solver, convenient to carry and easy to hold. Its continuous memory retains data and program instructions indefinitely until you choose to reset it. Though sophisticated, it requires no prior...

The HP-15C: A Problem Solver 13 The display format used in this handbook is • 4 (the decimal point is ―fixed‖ to show four decimal places) unless otherwise mentioned. If your calculator does not show four decimal places, you may want to press ´• 4 to match the displays in the examples. Manual Soluti...

14 The HP-15C: A Problem Solver The time an object takes to fall to the ground (ignoring air friction) is given by the formula g 2 h t  , where t = time in seconds, h = height in meters, g = the acceleration due to gravity, 9.8 m/s 2 . Example: Compute the time taken by a stone falling from the top...

The HP-15C: A Problem Solver 15 Keystrokes Display |¥ 000- Sets HP-15C to Program mode. ( PRGM annunciator on.) ´ CLEAR M 000- Clears program memory. (This step is optional here.) ´bA 001-42,21,11 Label "A" defines the beginning of the program. 2 002- 2 * 003- 20 9 004- 9 The same keys you p...

16 The HP-15C: A Problem Solver With this program loaded, you can quickly calculate the time of descent of an object from different heights. Simply key in the height and press ´A . Find the time of descent for objects released from heights of 100 m, 2 m, 275 m, and 2,000 m. The answers are: 4.5175 s...

18 Section 1 Getting Started Power On and Off The = key turns the HP-15C on and off. * To conserve power, the calculator automatically turns itself off after a few minutes of inactivity. Keyboard Operation Primary and Alternate Functions Most keys on your HP-15C perform one primary and two alternate...

Section 1: Getting Started 19 Notice that when you press the ´ or | prefix key, an f or g annunciator appears and remains in the display until a function key is pressed to complete the sequence. Prefix Keys A prefix key is any key which must precede another key to complete the key sequence for a fun...

20 Section 1: Getting Started Keystrokes Display 6.6262 6.6262 ‛ 6.6262 00 The 00 prompts you to key in the exponent. 3 6.6262 03 (6.6262×10 3 ). 4 6.6262 34 (6.6262×10 34 ). “ 6.6262 -34 (6.6262×10 -34 ). v 6.6262 -34 Enters number. 50 * 3.3131 -32 Joule-seconds. Note: Decimal digits from the manti...

Section 1: Getting Started 21 Clearing Sequence Effect ´ CLEAR M In Run mode: Repositions program memory to line 000. In Program mode: Deletes all program memory. ´ CLEAR Q Clears all data storage registers. ´ CLEAR u * Clears any prefix from a partially entered key sequence. * Also temporarily disp...

22 Section 1: Getting Started Calculations One-Number Functions A one-number function performs an operation using only the number in the display. To use any one-number function, press the function key after the number has been placed in the display. Keystrokes Display 45 45 |o 1.6532 Two-Number Func...

Section 1: Getting Started 23 Example: Calculate (9 + 17  4) ÷ 4. Keystrokes Display 9 v 9.0000 Digit entry terminated. 17 + 26.0000 (9 + 17). 4 - 22.0000 (9 + 17 – 4). 4 ÷ 5.5000 (9 + 17 – 4) ÷ 4. Even more complicated problems are solved in the same manner-using automatic storage and retrieval of...

24 Section 2 Numeric Functions This section discusses the numeric functions of the HP-15C (excluding statistics and advanced functions). The nonnumeric functions are discussed separately (digit entry in section 1, stack manipulation in section 3, and display control in section 5). The numeric functi...

Section 2: Numeric Functions 25 Keystrokes Display 123.4567 |‘ 123.0000 |K “ |‘ -123.0000 Reversing the sign does not alter digits. |K ´q -0.4567 1.23456789 “ |& -1.2346 ´ CLEAR u (release) 1234600000 Temporarily displays all -1.2346 digits in the mantissa. |a 1.2346 One-Number Functions One-num...

26 Section 2: Numeric Functions Trigonometric Operations Trigonometric Modes. The trigonometric functions operate in the trigonometric mode you select. Specifying a trigonometric mode does not convert any number already in the calculator to that mode; it merely tells the calculator what unit of meas...

Section 2: Numeric Functions 27 Hours.Decimal Hours Hours.Minutes Seconds Decimal Seconds (H.h) (H.MMSSs) Degrees.Decimal Hours Degrees.Minutes Seconds Decimal Seconds (D.d) (D.MMSSs) Hours/Degrees-Minutes-Seconds Conversion. Pressing ´ h converts the number in the display from a decimal hours/degre...

28 Section 2: Numeric Functions Logarithmic Functions Natural Logarithm. Pressing |Z calculates the natural logarithm of the number in the display; that is, the logarithm to the base e. Natural Antilogarithm. Pressing ' calculates the natural antilogarithm of the number in the display; that is, rais...

Section 2: Numeric Functions 29 Two-Number Functions The HP-15C performs two-number math functions using two values entered sequentially into the display. If you are keying in both numbers, remember that they must be separated by v or any other function – like | ‘ or ∕ – that terminates digit entry....

30 Section 2: Numeric Functions For example, to find the sales tax at 3% and total cost of a $15.76 item: Keystrokes Display 15.76 v 15.7600 Enters the base number (the price). 3 |k 0.4728 Calculates 3% of $15.76 (the tax). + 16.2328 Total cost of item ($15.76 + $0.47). Percent Difference. The ∆ fun...

Section 2: Numeric Functions 31 Rectangular Conversion. Pressing ´; (rectangular) converts a set of polar coordinates (magnitude r angle θ) into rectangular coordinates (x, y) . θ must be entered first then r. Upon executing ´; , x will be displayed first; press ® to display y . Keystrokes Display |...

32 Section 3 The Automatic Memory Stack, LAST X, and Data Storage The Automatic Memory Stack and Stack Manipulation HP operating logic is based on a mathematical logic known as ―Polish Notation,‖ developed by the noted Polish logician Jan Łukasiewicz (Wookashye'veech ) (1878-1956). Conventional alge...

Section 3: The Memory Stack, LAST X, and Data Storage 33 Any number that is keyed in or results from the execution of a numeric function is placed into the display (X-register). This action will cause numbers already in the stack to lift, remain in the same register, or drop, depending upon both the...

Section 3: The Memory Stack, LAST X, and Data Storage 35 The LAST X Register and K The LAST X register, a separate memory register, preserves the value that was last in the display before execution of a numeric operation. * Pressing |K (LAST X) places a copy of the contents of the LAST X register in...

36 Section 3: The Memory Stack, LAST X, and Data Storage Keystrokes Display * 287.0000 Reverses the function that produced the wrong answer. 13.9 + 20.6475 The correct answer. Calculator Functions and the Stack When you want to key in two numbers, one after the other, you press v between entries of ...

Section 3: The Memory Stack, LAST X, and Data Storage 37 lost T z z z z Z z z z z Y y y y y X 7 0 6 y 6 Keys: |` 6 Y Order of Entry and the v Key An important aspect of two-number functions is the positioning of the numbers in the stack. To execute an arithmetic function, the numbers should be posit...

38 Section 3: The Memory Stack, LAST X, and Data Storage Nested Calculations The automatic stack lift and stack drop make it possible to do nested calculations without using parentheses or storing intermediate results. A nested calculation is solved simply as a series of one- and two-number operatio...

Section 3: The Memory Stack, LAST X, and Data Storage 39 T y y y y Z y x y x Y x 13 x 65 X 13 5 65 4 Keys: 5 * 4 T y y y y Z x y x y Y 65 x 69 x X 4 69 3 207 Keys: + 3 * Arithmetic Calculations With Constants There are three ways (without using a storage register) to manipulate the memory stack to p...

40 Section 3: The Memory Stack, LAST X, and Data Storage Example: Two close stellar neighbors of Earth are Rigel Centaurus (4.3 light-years away) and Sirius (8.7 light-years away). Use the speed of light, c (3.0×10 8 meters/second, or 9.5×10 15 meters/year), to figure the distances to these stars in...

Section 3: The Memory Stack, LAST X, and Data Storage 41 Loading the Stack with a Constant. Because the number in the T-register is replicated when the stack drops, this number can be used as a constant in arithmetic operations. T c c New constant generation. Z c c Y c c Drops to interact with X-reg...

42 Section 3: The Memory Stack, LAST X, and Data Storage Keystrokes Display * 1,150.0000 Population at the end of day 1. * 1,322.5000 Day 2. * 1,520.8750 Day 3. * 1,749.0063 Day 4. Storage Register Operations When numbers are stored or recalled, they are copied between the display (X-register) and t...

Section 3: The Memory Stack, LAST X, and Data Storage 43 The above are stack lift-enabling operations, so the number remaining in the X-register can be used for subsequent calculations. If you address a nonexistent register, the display will show Error 3 . Example: Springtime is coming and you want ...

44 Section 3: The Memory Stack, LAST X, and Data Storage The number in the register is determined as follows: For storage arithmetic, new contents of register = old contents of register   ×  number in display R 0 r T t R 0 r-x T t Z z Z z Y y Y y X x X x Keys: O-0 Recall Arithmetic . Recall arith...

Section 3: The Memory Stack, LAST X, and Data Storage 45 Example: Keep a running count of your newly blooming crocuses for two more days. Keystrokes Display 8 O 0 8.0000 Places the total number of blooms as of day 2 in R 0 . 4 O + 0 4.0000 Day 3: adds four new blooms to those already blooming. 3 O +...

46 Section 3: The Memory Stack, LAST X, and Data Storage 2. Use arithmetic with constants to calculate the remaining balance of a $1000 loan after six payments of $100 each and an interest rate of 1% (0.01) per payment period. Procedure: Load the stack with (1 + i ), where i = interest rate, and key...

47 Section 4 Statistics Functions A word about the statistics functions: their use is based on an understanding of memory stack operation (Section 3). You will find that order of entry is important for most statistics calculations. Probability Calculations The input for permutation and combination c...

48 Section 4: Statistics Functions How many different four-card hands can be dealt from a deck of 52 cards? Keystrokes Display 52 v 4 4 Fifty-two ( y ) cards dealt four ( x ) at a time. |c 270,725.0000 Number of different hands possible. The maximum size of x or y is 9,999,999,999. Random Number Gen...

Section 4: Statistics Functions 49 Keystrokes Display l´# 0.2809 Recall last random number generated, which is the new seed. (The ´ may be omitted.) Accumulating Statistics The HP-15C performs one- and two-variable statistical calculations. The data is first entered into the Y- and X-registers. Then...

50 Section 4: Statistics Functions In some cases involving x or y data values that differ by a relatively small amount, the calculator cannot compute s, r, linear regression, or ŷ, and will display Error 2 . This will not happen, however, if you normalize the data by keying in only the difference be...

52 Section 4: Statistics Functions Correcting Accumulated Statistics If you discover that you have entered data incorrectly, the accumulated statistics can be easily corrected. Even if only one value of an ( x, y ) data pair is incorrect, you must delete and re-enter both values. 1. Key the incorrec...

Section 4: Statistics Functions 53 Mean The ’ function computes the arithmetic mean (average) of the x -and y - values using the formulas shown in appendix A and the statistics accumulated in the relevant registers. When you press |’ the contents of the stack lift (two registers if stack lift is ena...

54 Section 4: Statistics Functions Example: Calculate the standard deviation about the mean calculated above. Keystrokes Display |S 31.62 Standard deviation about the mean nitrogen application, x. ® 1.24 Standard deviation about the mean grain yield, y. Linear Regression Linear regression is a stati...

Section 4: Statistics Functions 55 Example: Find the y -intercept and slope of the linear approximation of the data and compare to the plotted data on the graph below. Keystrokes Display ´L 4.86 y -intercept of the line. ® 0.04 Slope of the line. Linear Estimation and Correlation Coefficient When yo...

56 Section 4: Statistics Functions Linear Estimation. With the statistics accumulated, an estimated value for y, denoted ŷ , can be calculated by keying in a proposed value for x and pressing ´j . An Estimated value for x (denoted x ˆ ) can be calculated as follows: 1. Press ´L . 2. Key in the known...

Section 4: Statistics Functions 57 Keystrokes Display 70 ´j 7.56 Predicted grain yield in tons/hectare. ® 0.99 The original data closely approximates a straight line. Other Applications Interpolation. Linear interpolation of tabular values, such as in thermodynamics and statistics tables, can be car...

58 Section 5 The Display and Continuous Memory Display Control The HP-15C has three display formats – • , i , and ^ – that use a given number (0 through 9) to specify display format. The illustration below shows how the number 123,456 would be displayed specified to four places in each possible mode...

Section 5: The Display and Continuous Memory 59 Scientific Notation Display i (scientific) format displays a number in scientific notation. The sequence ´i n specifies the number of decimal places to be shown. Up to six decimal places can be shown since the exponent display takes three spaces. The d...

60 Section 5: The Display and Continuous Memory Mantissa Display Regardless of the display format, the HP-15C always internally holds each number as a 10-digit mantissa and a two-digit exponent of 10. For example, π is always represented internally as 3.141592654×10 00 , regardless of what is in the...

Section 5: The Display and Continuous Memory 61 Digit Separators The HP-15C is set at power-up so that it separates integral and fractional portions of a number with a period (a decima l point), and separates groups of three digits in the integer portion with a comma. You can reverse this setting to...

62 Section 5: The Display and Continuous Memory Low-Power Indication When a flashing asterisk, which indicates low battery power, appears in the lower left-hand side of the display, there is no reason to panic. You still have plenty of calculator time remaining: at least 10 minutes if you continuous...

Section 5: The Display and Continuous Memory 63 Resetting Continuous Memory If at any time you want to reset (entirely clear) the HP-15C Continuous Memory: 1. Turn the calculator off. 2. Press and hold the = key, then press and hold the - key. 3. Release the = key, then the - key. (This convention i...

66 Section 6 Programming Basics The next five sections are dedicated to explaining aspects of programming the HP-15C. Each of these programming sections will first discuss basic techniques (The Mechanics), then give examples for the implementation of these techniques (Examples), and lastly discuss f...

Section 6: Programming Basics 67 Location in Program Memory . Program memory – and therefore the calculator's position in program memory – is demarcated by line numbers. Line 000 marks the beginning of program memory and cannot be used to store an instruction. The first line that contains an instruc...

68 Section 6: Programming Basics Keystrokes Display 2 002- 2 * 003- 20 9 004- 9 Given h in the X-register, lines 002 to 008 calculate . 005- 48 8 006- 8 9 .8 2 h . ÷ 007- 10 ¤ 008- 11 Program End. There are three possible endings for a program:  | n (return) will end a program, return to line 000, ...

Section 6: Programming Basics 69 Keystrokes Display |¥ Run mode; no PRGM annunciator displayed. (The display will depend on any previous result.) The position in program memory does not change when modes are switched. Should the calculator be shut off, it always ―wakes up‖ in Run mode. Executing a P...

70 Section 6: Programming Basics This is the method used above, where h was placed in the X-register before running the program. No v instruction is necessary because program execution (here: ´A ) both terminates digit entry and enables the stack lift. The above program then multiplied the contents ...

72 Section 6: Programming Basics Keystrokes Display ´bA 001-42,21,11 Assigns this program the label ―A‖. O 0 002- 44 0 Stores the contents of X-register into R 0 . r must be in the X- register before running the program. |x 003- 43 11 Squares the contents of the X- register (which will be r ). |$ 00...

74 Section 6: Programming Basics Keystrokes Display 4 4 Enter h of third can. ¦ 254.4690 VOLUME of third can. 240.3318 SURFACE AREA of third can. l 1 133.5177 Sum of BASE AREAS. l 2 939.3362 Sum of VOLUMES. l 3 769.6902 Sum of SURFACE AREAS. The preceding program illustrates the basic techniques of ...

Section 6: Programming Basics 75 Keycode 25: second row, fifth key. Memory Configuration Understanding memory configuration is not essential to your use of the HP-15C. It is essential, however, for obtaining maximum efficiency in memory and programming use. The more you program, the more useful this...

76 Section 6: Programming Basics Memory is reallocated by telling the calculator which data storage register shall be the highest data register; all other registers are left for programming and advanced functions. Keystrokes Display 60 ´ m % * 60.0000 R 60 and below allocated to data storage; five (...

Section 6: Programming Basics 77 Keystrokes Display 1 ´ m % 1.0000 R 1 and R 0 allocated for data storage; R 2 to R 65 available for programming and advanced functions. 19 ´ m% 19.0000 Original allocation: R 19 (R .9 ) and below for data storage; R 20 , to R 65 for programming and advanced functions...

78 Section 6: Programming Basics corresponding label. If need be, the search will wrap around at the end of program memory and continue at line 000. When it encounters an appropriate label, the search stops and execution begins. If a label is encountered as part of a running program, it has no effec...

Section 6: Programming Basics 79 For example, ´b´A becomes ´bA , ´m´% becomes ´m% , and O´# becomes O# . The removal of the ´ is not ambiguous because the ´ -shifted function is the only logical one in these cases. The keycodes for such instructions do not include the extraneous ´ even if you do key...

80 Section 6: Programming Basics Example: Write a program for 5 x 4 + 2 x 3 as (((5 x + 2 ) x ) x ) x, then evaluate for x = 7 Keystrokes Display | ¥ 000- Assumes position in memory is line 000. If it is not, clear program memory. ´ b B 001-42,21,12 5 002- 5 * 003- 20 5 x . 2 004- 2 + 005- 40 5 x + ...

Section 6: Programming Basics 81 Problems 1. The village of Sonance has installed a 12-o'clock whistle in the firehouse steeple. The sound level at the firehouse door, 3.2 meters from the whistle, is 138 decibels. Write a program to find the sound level at various distances from the whistle. Use the...

82 Section 7 Program Editing There are many reasons to modify a program after you've already stored it: you might want to add or delete an instruction (like O , © , or ¦ ), or you might even find some errors! The HP-15C is equipped with several editing features to make this process as easy as possib...

Section 7: Program Editing 83 The Back Step ( ‚ ) Instruction. To move one line backwards in program memory, press ‚ ( back step ) in Program or Run mode. This function is not programmable. ‚ will scroll (with the key held down) in Program mode. Program instructions are not executed. Deleting Progra...

Section 7: Program Editing 85 Keystrokes Display − 019- 40 Line 020 deleted. | ‚ (hold) 016- 45 4 The next line to edit is line 016 ( l 4). − 015- 20 Line 016 deleted. l 2 016- 45 2 Line 016 changed to l 2. t “ 011 (or hold ‚ ) 011-44,40, 2 Moves to line 011 ( O+ 2). − 010- 42 31 Line 011 deleted. |...

86 Section 7: Program Editing you can check the program by executing it stepwise. This is done by pressing  in Run mode. Keystrokes Display | ¥ Run mode. ´ CLEAR Q Clear storage registers. t A Move to first line of program A. 8 O 1 8.0000 Store a can height. 2.5 2.5 Enter a can radius.  (hold) 001...

Section 7: Program Editing 87 Insertions and Deletions After an insertion, the display will show the instruction you just added. After a deletion, the display will show the line prior to the deleted (now nonexistent) one. If all space available in memory is occupied, the calculator will not accept a...

88 Section 7: Program Editing Keystrokes Display ´ b . 1 001-42,21,.1 ´ • 2 002-42, 7, 2 1 003- 1 . 004- 48 0 005- 0 Interest . 7 006- 7 5 007- 5 ® 008- 34 y 009- 14 (1 + i ) n * 010- 20 PV (1 + i ) n | n 011- 43 32 Load the program and find the future value of $1,000 invested for 5 years; of $2,300...

90 Section 8 Program Branching and Controls Although the instructions in a program are normally executed sequentially, it is often desirable to transfer execution to a part of the program other than the next line. Branching in the HP-15C may be simple , or it may depend on a certain condition . By b...

Section 8: Program Branching and Controls 91 of this loop can be controlled by a conditional branch, an ¦ instruction (written into the loop), or simply by pressing any key during execution (which stops the program). Conditional Tests Another way to alter the sequence of program execution is by a co...

92 Section 8: Program Branching and Controls Following a conditional test, program execution follows the "Do if True" Rule: it proceeds sequentially if the condition is true, and it skips one instruction if the condition is false. A t instruction is often placed right after a conditional tes...

Section 8: Program Branching and Controls 93 Examples Example: Branching and Looping A radiobiology lab wants to predict the diminishing radioactivity of a test amount of 131 I, a radioisotope. Write a program to figure the radioactivity at 3-day intervals until a given limit is reached. The formula...

96 Section 8: Program Branching and Controls Keystrokes Display | ¥ 000- Program mode. ´ bB 001-42,21,12 Start at "B" if payments to be made at the beginning. | " 0 002-43, 5, 0 Flag 0 clear (false); indicates advance payments. t 1 003- 22 1 Go to main routine. ´ b E 004-42,21,15 Start a...

Section 8: Program Branching and Controls 97 Now run the program to find the total amount needed in an account from which you want to take $250/month for 48 months. Enter the periodic interest rate as a decimal fraction, that is, 0.005 per month. First find the sum needed if payments will be made at...

98 Section 8: Program Branching and Controls Looping Looping is an application of branching which uses a t instruction to repeat a portion of the program. A loop can continue indefinitely, or may be conditional. A loop is frequently used to repeat a calculation with different variables. At the same ...

Section 8: Program Branching and Controls 99 In this way, a program can accommodate two different modes of input, such as degrees and radians, and make the correct calculation for the mode chosen. You set a flag if a conversion needs to be made, for instance, and clear it if no conversion is needed....

100 Section 8: Program Branching and Controls Flag 9. An overflow condition (described on page 61) automatically sets flag 9. Flag 9 causes the display to blink or, if a program is running, waits until execution is complete and then starts blinking the display. Flag 9 may be cleared in three ways: ...

101 Section 9 Subroutines When the same set of instructions needs to be used at more than one point in a program, memory space can be conserved by storing those instructions as a single subroutine. The Mechanics Go To Subroutine and Return The G ( go to subroutine ) instruction is executed in the sa...

102 Section 9: Subroutines Subroutine Limits A subroutine can call up another subroutine, and that subroutine can call up yet another subroutine. This ―subroutine nesting‖—the execution of a subroutine within a subroutine—is limited to stack of subroutines seven levels deep (this does not count the ...

Section 9: Subroutines 103 MAIN PROGRAM |¥ ´ CLEAR M (Not programmable.) 000- 001- ´ b 9 Start main program. 002- | R Radians mode. 003- O 0 Stores x 2 in R 0 . 004- ® Brings x 1 into X; x 2 into Y. 005- O - 0 ( x 2 - x 1 ) in R 0 . 006- G .3 Transfer to subroutine ―.3‖ with x 1 . Return from subrou...

Section 9: Subroutines 105 Further Information The Subroutine Return The pending return condition means that the n instruction occurring subsequent to a G instruction causes a return to the line following the G rather than a return to line 000. This is what makes a subroutine useful and reuseable in...

106 Section 10 The Index Register and Loop Control The Index register (R I ) is a powerful tool in advanced programming of the HP-15C. In addition to storage and recall of data the Index register can use an index number to:  Count and control loops.  Indirectly address storage registers, including...

Section 10: The Index Register and Loop Control 107 Indirect Program Control With the Index Register The V key is used for all forms of indirect program control other than indirect register addressing. Hence, V (not % ) is used for indirect program branching, indirect display format control, and ind...

108 Section 10: The Index Register and Loop Control Indirect Addressing If R I contains: % will address: t V or GV will transfer to:* 21 R 21 ´ b B 22 R 22 " " C 23 R 23 " " Á 24 R 24 " " E ⋮ ⋮ — 65 R 65 — * For R I  0 only. Index Register Arithmetic Direct. O or l { + , - ,...

Section 10: The Index Register and Loop Control 109 To Labels. If the R I value is positive , t V and G V will transfer execution to the label which corresponds to the number in the Index register (see the above table). For instance, if the Index register contains 20.00500, then a tV instruction wil...

110 Section 10: The Index Register and Loop Control For example, the number 0.05002 in a storage register represents: nnnnn x x x y y 0.0 5 0 0 2 Start count at zero. Count by twos. Count up to 50. I and e Operation . Each time a program encounters I or e it increments or decrements nnnnn (the integ...

Section 10: The Index Register and Loop Control 111 False (nnnnn > xxx) True (nnnnn  xxx) instruction ´sV loop t. 1 Instruction exit loop For e : given nnnnn.xxxyy , decrement nnnnn to nnnnn - yy , compare it to xxx, and skip the next program line if the new value satisfies nnnnn ≤ xxx . This al...

112 Section 10: The Index Register and Loop Control Keystrokes Display l % 2.6458 Indirectly recalls contents of R .2 . ´ X .2 2.6458 Check: same contents recalled by directly addressing R .2 . Exchanging the X-Register Keystrokes Display ´ X V 12.3456 Exchanges contents of R I and X- register. l V ...

114 Section 10: The Index Register and Loop Control Keystrokes Display 15 “ O V ´ A -15.0000 Branch line number. 2.0000 Running program loop counter = 3. 84.0896 5.0000 Loop counter = 2. 64.8420 8.0000 Loop counter = 1. 50.0000 50.0000 Loop counter = 0; program ends. Example: Display Format Control ...

Section 10: The Index Register and Loop Control 115 To display fixed point notation for all possible decimal places on the HP-15C: Keystrokes Display | ¥ Run mode. ´ B 9.000000000 8.00000000 7.0000000 6.000000 5.00000 4.0000 3.000 2.00 1.0 0. Display at ´© instruction. 0. Display when program halts....

116 Section 10: The Index Register and Loop Control I and e For the purpose of loop control, the integer portion (the counter value) of the stored control number can be up to five digits long ( nnnnn.xxxyy ). The counter value ( nnnnn ) is zero if not specified otherwise. xxx, in the decimal portion...

120 Section 11 Calculating With Complex Numbers The HP-15C enables you to calculate with complex numbers, that is, numbers of the form a + ib , where a is the real part of the complex number, b is the imaginary part of the complex number, and 1   i . As you will see, the beauty of calculating with...

Section 11: Calculating With Complex Numbers 121 Complex mode is activated 1) automatically, when executing ´ V or ´ } ; or 2) by setting flag 8, the Complex mode flag ( |F 8). When the calculator is in Complex mode, the C annunciator in the display is lit. This tells you that flag 8 is set and the ...

122 Section 11: Calculating With Complex Numbers Example: Add 2 + 3 i and 4 + 5 i . (The operations are illustrated in the stack diagrams following the keystroke listing.) Keystrokes Display ´ • 4 2 v 2.0000 Keys real part of first number into (real) Y-register. 3 3 Keys imaginary part of first numb...

124 Section 11: Calculating With Complex Numbers Stack Lift in Complex Mode Stack lift operates on the imaginary stack as it does on the real stack (the real stack behaves identically in and out of Complex mode). The same functions that enable, disable, or are neutral to lifting of the real stack wi...

Section 11: Calculating With Complex Numbers 125 of Complex mode. Instead, you can do either of the following:  Multiply by -1.  If you don't want to disturb the rest of the stack, press “ ´ } “ ´ } . To find the negative of only one part of a complex number in the X -register:  Press “ to negate...

126 Section 11: Calculating With Complex Numbers Clearing the Imaginary X-Register. To clear the number in the imaginary X-register, press ´ } , then press − . Press ´ } again to return the zero, or any new number keyed in, to the imaginary X-register. Example: Replace -1 -8 i by -1 + 5 i . Re Im Re...

Section 11: Calculating With Complex Numbers 127 Entering Complex Numbers with − . The clearing functions − and ` can also be used with } as an alternative method of entering (and clearing) complex numbers. Using this method, you can enter a complex number using only the X-register, without affectin...

128 Section 11: Calculating With Complex Numbers Re Im Re Im Re Im Re Im T a b a b a b a b Z c d c d c d c d Y e f e f e f e f X 7 8 0 8 9 8 17 144 Keys: − 9 | x Entering a Real Number You have already seen two ways of entering a complex number. There is a shorter way to enter a real number: simply ...

Section 11: Calculating With Complex Numbers 129 Entering a Pure Imaginary Number There is a shortcut for entering a pure imaginary number into the X -register when you are already in Complex mode: key in the (imaginary) number and press ´ } Example: Enter 0 + 10 i (assuming the last function execut...

130 Section 11: Calculating With Complex Numbers Storing and Recalling Complex Numbers The O and l functions act on the real X-register only; therefore, the imaginary part of a complex number must be stored or recalled separately. The keystrokes to do this can be entered as part of a program and exe...

Section 11: Calculating With Complex Numbers 131 One-Number Functions The following functions operate on both the real and imaginary parts of the number in the X-register, and place the real and imaginary parts of the answer back into those registers. ¤ x N o ∕ @ ' a : ; All trigonometric and hyperb...

132 Section 11: Calculating With Complex Numbers Conditional Tests For programming, the four conditional tests below will work in the complex sense: ~ and T 0 compare the complex number in the (real and imaginary) X-registers to 0 + 0 i , while T 5 and T 6 compare the complex numbers in the (real an...

Section 11: Calculating With Complex Numbers 133 Complex Results from Real Numbers In the preceding examples, the entry of complex numbers had ensured the (automatic) activation of Complex mode. There will be times, ho wever, when you will need Complex mode to perform certain operations on real numb...

134 Section 11: Calculating With Complex Numbers a + ib = r (cos θ + i sin θ) = re iθ (polar) r  θ (phasor) ; and : can be used to interconvert the rectangular and polar forms of a complex number. They operate in Complex mode as follows: ´ ; converts the polar (or phasor) form of a complex numbe r ...

Section 11: Calculating With Complex Numbers 135 Example: Find the sum 2(cos 65° + i sin 65°) + 3(cos 40° + i sin 40°) and express the result in polar form, (In phasor form, evaluate 2  65° + 3  40°.) Keystrokes Display | D Sets Degrees mode for any polar-rectangular conversions. 2 v 2.0000 65 ´ V...

136 Section 11: Calculating With Complex Numbers Keystrokes Display 2 ´ } 0.0000 2 i . Display shows real part. 8 “ v -8.0000 6 ´ V -8.0000 -8 + 6 i . 3 Y 352.0000 (-8 + 6 i ) 3 . * -1.872.0000 2 i (-8 + 6 i ) 3 . 4 v 4.0000 5 ¤ 2.2361 2 “ * -4.4721 5 2  . ´ V 4.0000 i 5 2 4  . ÷ -295.4551 i i i 5...

Section 11: Calculating With Complex Numbers 137 For Further Information The HP-15C Advanced Functions Handbook presents more detailed and technical aspects of using complex numbers in various functions with the HP-15C. Applications are included. The topics include:  Accuracy considerations.  Prin...

138 Section 12 Calculating With Matrices The HP-15C enables you to perform matrix calculations, giving you the capability to handle advanced problems with ease. The calculator can work with up to five matrices, which are named A through E since they are accessed using the corresponding A through E k...

Section 12: Calculating with Matrices 139 Keystrokes Display | " 8 Deactivates Complex mode. 2 v ´ m A 2.0000 Dimensions matrix A to be 2×2. ´ > 1 2.0000 Prepares for automatic entry of matrix elements in User mode. ´ U 2.0000 (Turns on the USER annunciator.) 3.8 O A A 1,1 Denotes matrix A , ...

140 Section 12: Calculating with Matrices Keystrokes Display l > B b 2 1 Enters descriptor for B , the 2×1 constant matrix. l > A A 2 2 Enters descriptor for A , the 2×2 coefficient matrix, into the X-register, moving the descriptor for B into the Y-register. ÷ running Temporary display while ...

Section 12: Calculating with Matrices 141 Matrix inversion, for example, can be performed on an 8×8 matrix with real elements (or on a 4×4 matrix with complex elements, as described later * ). To conserve memory, all matrices are initially dimensioned as 0×0. When a matrix is dimensioned or redimens...

142 Section 12: Calculating with Matrices Example: Dimension matrix A to be a 2×3 matrix. Keystrokes Display 2 v 2.0000 Keys number of rows into Y-register. 3 3 Keys number of columns into X-register. ´mA 3.0000 Dimensions matrix A to be 2×3. Displaying Matrix Dimensions There are two ways you can d...

Section 12: Calculating with Matrices 143 If you redimension a matrix to a larger size, elements with the value 0 are added at the end as required by the new dimensions. For example, if the same 2×3 matrix is re dimensioned, to 2×4, then When you have finished calculating with matrices, you'll proba...

144 Section 12: Calculating with Matrices To store or recall sequential elements of a matrix: 1. Be sure the matrix is properly dimensioned. 2. Press ´ > 1. This stores 1 in both storage registers R 0 and R 1 , so that elements will be accessed starting at row 1, column 1. 3. Activate User mode b...

Section 12: Calculating with Matrices 145 Keystrokes Display ´ > 1 Sets beginning row and column numbers in R 0 and R 1 to 1. (Display shows the previous result.) ´ U Activates User mode. 1 O A A 1,1 Row 1, column 1 of A . (Displayed momentarily while A key held down.) 1.0000 Value of a 11 . 2 O ...

146 Section 12: Calculating with Matrices Using R 0 and R 1 . To access a particular matrix element, store its row number in R 0 and its column number in R 1 . These numbers won't change automatically (unless the calculator is in User mode).  To recall the element value (after storing the row and c...

Section 12: Calculating with Matrices 147 Example: Recall the element in row 2, column 1 of matrix A from the previous example. Use the stack registers. Keystrokes Display 2 v 1 1 Enters row number into Y-register and column number into X-register. l | A 4.0000 Value of a 21 . Storing a Number in Al...

148 Section 12: Calculating with Matrices operate on the matrices whose descriptors are placed in the X-register and (for some operations) the Y-register. Two matrix operations – calculating a determinant and solving the matrix equation AX = B – involve calculating an LU decomposition (also known as...

Section 12: Calculating with Matrices 149 While the key used for any matrix operation that stores a result in the result matrix is held down, the descriptor of the result matrix is displayed. If the key is released within about 3 seconds, the operation is performed, and the descriptor of the result ...

150 Section 12: Calculating with Matrices One-Matrix Operations: Sign Change, Inverse, Transpose, Norms, Determinant Keystroke(s) Result in X-register Effect on Matrix Specified in X-register Effect on Result Matrix “ No change. Changes sign of all elements. None. ‡ ∕ ( ´∕ in User Mode) Descriptor o...

Section 12: Calculating with Matrices 151 Example: Calculate the transpose of matrix B . Matrix B was set in preceding examples to . 9 5 4 3 2 1        B Keystrokes Display l > B b 2 3 Displays descriptor of 2×3 matrix B . ´ > 4 b 3 2 Descriptor of 3×2 transpose. Matrix B (which you can...

152 Section 12: Calculating with Matrices Operation Elements of Result Matrix* Matrix in Y-Register Scalar in Y-Register Scalar in X-Register Matrix in X-Register + Adds scalar value to each matrix element. * Multiplies each matrix element by scalar value. - Subtracts scalar value from each matrix e...

Section 12: Calculating with Matrices 153 Keystrokes Display 1 - b 2 3 Subtracts 1 from the elements of matrix B and stores those values in the same elements of B . The result (which you can view using lB in User mode) is          17 9 7 5 3 1 B . Arithmetic Operations With matrix descripto...

154 Section 12: Calculating with Matrices Keystrokes Display - C 2 3 Calculates B - A and stores values in redimensioned result matrix C . The result is        8 4 3 2 1 0 C Matrix Multiplication With matrix description in both the X- and Y-registers, you can calculate three different matrix ...

156 Section 12: Calculating with Matrices Solving the Equation AX = B The ÷ function is useful for solving matrix equations of the form AX = B , where A is the coefficient matrix, B is the constant matrix, and X is the solution matrix. The descriptor of the constant matrix B should be entered in the...

Section 12: Calculating with Matrices 157 Week 1 2 3 Total Weight (kg) 274 233 331 Total Value $120.32 $112.96 $151.36 Silas knows that he received $0.24 per kilogram for his cabbage and $0.86 per kilogram for his broccoli. Use matrix operations to deter mine the weights of cabbage and broccoli he d...

158 Section 12: Calculating with Matrices Keystrokes Display 274 OB 274.0000 Stores b 11 . * 233 OB 233.0000 Stores b 12 . 331 OB 331.0000 Stores b 13 . 120.32 OB 120.3200 Stores b 21 . 112.96 OB 112.9600 Stores b 22 . 151.36 OB 151.3600 Stores b 23 . ´< Á 151.3600 Designates matrix D as result m...

Section 12: Calculating with Matrices 159 Silas' deliveries were: Week 1 2 3 Cabbage (kg) 186 141 215 Broccoli (kg) 88 92 116 Calculating the Residual The HP-15C enables you to calculate the residual, that is, the matrix Residual = R–YX where R is the result matrix and X and Y are the matrices speci...

160 Section 12: Calculating with Matrices Using Matrices in LU Form As noted earlier, two matrix operations (calculating a determinant and solving the matrix equation ( AX = B ) create an LU decomposition of the matrix specified in the X-register. The descriptor of such a matrix has two dashes follo...

Section 12: Calculating with Matrices 161 Instead, calculations with complex matrices are performed by using real matrices derived from the original complex matrices – in a manner to be described below – and performing certain transformations in addition to the regular matrix operations. These trans...

162 Section 12: Calculating with Matrices Suppose you need to do a calculation with a complex matrix that is not written as the sum of a real matrix and an imaginary matrix – as was the matrix Z in the example above – but rather written with an entire complex number in each element, such as     ...

Section 12: Calculating with Matrices 163 Example: Store the complex matrix            i i i i 8 3 5 1 2 7 3 4 Z in the form Z C , since it is written in a form that shows Z C . Then transform Z C into the form Z P . You can do this by storing the elements of Z C in matrix A and then usin...

164 Section 12: Calculating with Matrices Matrix A now represents the complex matrix Z in Z P form: P art Imag i n ary P art Real . 8 5 2 3 3 1 7 4 } }                  P Z A The Complex Transformations Between Z P and Z An additional transformation must be done when you want to cal...

Section 12: Calculating with Matrices 165 Inverting a Complex Matrix You can calculate the inverse of a complex matrix by using the fact that ( ) -1 = ( -1 ). To calculate inverse, Z -1 , of a complex matrix Z : 1. Store the elements of Z in memory, in the form either of Z P or of Z C 2. Recall the ...

166 Section 12: Calculating with Matrices Keystrokes Display ´ < B A 4 4 Designates B as the result matrix. ∕ b 4 4 Calculates ( ) -1 = ( -1 ) and places the result in matrix B . ´> 3 b 4 2 Transforms ( -1 ) into ( -1 ) P . The representation of Z -1 in partitioned form is contained in matrix ...

Section 12: Calculating with Matrices 167 8. Press * to calculate X P = ( YX ) P . The values of these matrix elements are placed in the result matrix, and the descriptor of the result matrix is placed in the X-register. 9. If you want the product in the form ( YX ) C , press |c Note that you don't ...

168 Section 12: Calculating with Matrices Writing down the elements of C ,   P 1 10 11 10 11 11 10 1 0 0 5 0 0 . 1 1 0 0 0 0 0 . 1 1 0 8 0 0 0 . 3 1 0 0 0 0 0 . 1 0 0 0 0 . 1 1 0 0 0 0 0 . 4 1 0 8 5 0 0 . 2 0 0 0 0 . 1                                 ZZ C , where th...

Section 12: Calculating with Matrices 169 4. Recall the descriptor of the matrix representing A into the display. 5. If the elements of A were entered in the form of A C , press ´ p to transform A C into A P . 6. Press ´> 2 to transform A P into à . 7. Designate the result matrix; it must not be ...

170 Section 12: Calculating with Matrices In partitioned form,                                 0 0 0 5 an d 1 7 0 2 0 0 2 0 0 2 0 0 0 0 0 1 0 B A , where the zero elements correspond to real and imaginary parts with zero value. Keystrokes Display 4 v 2 ´mA 2.0000 Dime...

Section 12: Calculating with Matrices 171 Keystrokes Display ´> 2 A 4 4 Transforms A P into à . ´< C A 4 4 Designates matrix C as result matrix. ÷ C 4 1 Calculates X P and stores in C . |c C 2 2 Transforms X P into X C . lC 0.0372 Recalls c 11 . lC 0.1311 Recalls c 12 . lC 0.0437 Recalls c 21 ...

172 Section 12: Calculating with Matrices 1. Store the elements of A in memory, in the form either of A P or of A C . 2. Recall the descriptor of the matrix representing A into the display. 3. If the elements of A were entered in the form A C , press ´ p to transform A C into A P . 4. Press ´> 2 ...

Section 12: Calculating with Matrices 173 A problem using this procedure is given in the HP-15C Advanced Functions Handbook under Solving a Large System of Complex Equations. Miscellaneous Operations Involving Matrices Using a Matrix Element With Register Operations If a letter key specifying a matr...

174 Section 12: Calculating with Matrices  Pressing ´mV dimensions the matrix specified in R I according to the dimensions in the X- and Y-registers.  Pressing lmV recalls to the X- and Y-registers the dimensions of the matrix specified in R I .  Pressing GV or tV has the same result as pressing ...

176 Section 12: Calculating with Matrices Using Matrix Operations in a Program If the calculator is in User mode during program entry when you enter a O or l { A through E , % } instruction to store or recall a matrix element, a u replaces the dash usually displayed after the line number. When this ...

Section 12: Calculating with Matrices 177 The > 7 (row norm) and > 8 (Frobenius norm) functions also operate as conditional branching instructions in a program. If the X-register contains a matrix descriptor, these functions calculate the norm in the usual manner, and program execution continu...

178 Section 12: Calculating with Matrices Keystroke(s) Results result matrix. ´> 6 Calculates residual in result matrix. ´> 7 Calculates row norm of matrix specified in X-register. ´> 8 Calculates Frobenius or Euclidean norm of matrix specified in X-register. ´> 9 Calculates determinant ...

Section 12: Calculating with Matrices 179 Keystroke(s) Results O < Designates matrix specified in X-register as result matrix. ´ U Row and column numbers in R 0 and R 1 are automatically incremented each time O or l { A through E , % } is pressed. ∕ Inverts matrix specified in X-register. Stores ...

180 Section 13 Finding the Roots of an Equation In many applications you need to solve equations of the form f(x)= 0 . * This means finding the values of x that satisfy the equation. Each such value of x is called a root of the equation f(x) = 0 and a zero of the function f(x). These roots (or zeros...

182 Section 13: Finding the Roots of an Equation Keystrokes Display ´ b 0 001–42,21, 0 Begin with b instruction. Subroutine assumes stack loaded with x . 3 002– 3 - 003– 30 Calculate x – 3. * 004– 20 Calculate ( x – 3) x . 1 005– 1 0 006– 0 - 007– 30 Calculate ( x – 3) x – 10. | n 008– 43 32 In Run ...

186 Section 13: Finding the Roots of an Equation Fahr's ridget falls to the ground 9.2843 seconds after he hurls it—a remarkable toss. When No Root Is Found You have seen how the _ key estimates and displays a root of an equation of the form f(x) = 0. However, it is possible that an equation has no ...

Section 13: Finding the Roots of an Equation 187 Because the absolute-value function is minimum near an argument of zero, specify the initial estimates in that region, for instance 1 and -1. Then attempt to find a root. Keystrokes Display | ¥ Run mode. 1 v 1.0000 Initial estimates. 1 “ –1 ´ _ 1 Erro...

188 Section 13: Finding the Roots of an Equation The final case points out a potential deficiency in the subroutine rather than a limitation of the root-finding routine. Improper operations may sometimes be avoided by specifying initial estimates that focus the search in a region where such an outco...

Section 13: Finding the Roots of an Equation 189 If you have some knowledge of the behavior of the function f(x) as it varies with different values of x , you are in a position to specify initial estimates in the general vicinity of a zero of the function. You can also avoid the more troublesome ran...

190 Section 13: Finding the Roots of an Equation Keystrokes Display - 003– 30 * 004– 20 ( x – 6) x . 8 005– 8 + 005– 40 * 007– 20 (( x – 6) x + 8 ) x. 4 008– 4 * 009– 20 4 (( x – 6) x + 8) x. 7 010– 7 . 011– 48 5 012– 5 - 013– 30 |n 014– 43 32 It seems reasonable that either a tall, narrow box or a ...

192 Section 13: Finding the Roots of an Equation  Many functions exhibit special behavior when their arguments approach zero. You can check your function to determine values of x for which any argument within your function becomes zero, and then specify estimates at or near those values. Although t...

Section 13: Finding the Roots of an Equation 193 Restriction on the Use of _ The one restriction regarding the use of _ is that _ cannot be used recursively. That is, you cannot use _ in a subroutine that is called during the execution of _ . If this situation occurs, execution stops and Error 7 is ...

194 Section 14 Numerical Integration Many problems in mathematics, science, and engineering require calculating the definite integral of a function. If the function is denoted by f(x) and the interval of integration is a to b, the integral can be expressed mathematically as . ) ( dx x f I b a   Th...

Section 14: Numerical Integration 195 In Run mode: 2. Key the lower limit of integration ( a ) into the X-register, then press v to lift it into the Y-register. 3. Key the upper limit of integration ( b ) in to the X-register. 4. Press ´ f followed by the label of your subroutine. Example: Certain p...

196 Section 14: Numerical Integration Keystrokes Display | ¥ Run mode. 0 v 0.0000 Key lower limit, 0, into Y-register. | $ 3.1416 Key upper limit, π, into X-register. |R 3.1416 Specify Radians mode for trigonometric functions. Now you are ready to press ´f 0 to calculate the integral. When you do so...

198 Section 14: Numerical Integration Keystrokes Display [ 002– 23 Calculate sin θ . - 003– 30 Since a value of θ will be placed into the Y-register by the f algorithm before it executes this subroutine, the - operation at this point will calculate ( θ – sin θ ). \ 004– 24 Calculate cos ( θ – sin θ ...

Section 14: Numerical Integration 199 Find Si (2). Key in the following subroutine to evaluate the function f(x) = (sin x ) / x . * Keystrokes Display |¥ 000– Program mode. ´ b .2 001–42,21, .2 Begin subroutine with a b instruction. [ 002– 23 Calculate sin x . ® 003– 34 Since a value of x will be pl...

200 Section 14: Numerical Integration Accuracy of f The accuracy of the integral of any function depends on the accuracy of the function itself. Therefore, the accuracy of an integral calculated using f is limited by the accuracy of the function calculated by your subroutine. * To specify the accura...

202 Section 14: Numerical Integration If the uncertainty of an approximation is larger than what you choose to tolerate, you can decrease it by specifying a greater number of digits in the display format and repeating the approximation. * Whenever you want to repeat an approximation, you don't need ...

Section 14: Numerical Integration 203 In the preceding example, the uncertainty indicated that the approximation might be correct to only four decimal places. If we temporarily display all 10 digits of the approximation, however, and compare it to the actual value of the integral (actually, an appro...

204 Section 14: Numerical Integration Memory Requirements f requires 23 registers to operate. (Appendix C explains how they are automatically allocated from memory.) If 23 unoccupied registers are not available, f will not run and Error 10 will be displayed. A routine that combines f and _ also requ...

205 Appendix A Error Conditions If you attempt a calculation containing an improper operation – say division by zero – the display will show Error and a number. To clear an error message, press any one key. This also restores the display prior to the Error display. The HP-15C has the following error...

206 Appendix A: Error Conditions  x or y is noninteger;  x < 0 or y < 0;  x > y ;  x or y ≥ 10 10 . Error 1: Improper Matrix Operation Applying an operation other than a matrix operation to a matrix, that is, attempting a nonmatrix operation while a matrix is in the relevant register (w...

Appendix A: Error Conditions 207 Error 3: Improper Register Number or Matrix Element Storage register named is nonexistent or matrix element indicated is nonexistent. Error 4: Improper Line Number or Label Call Line number called for is currently unoccupied or nonexistent (>448); or you have atte...

208 Appendix A: Error Conditions + or - , where the dimensions are incompatible. * , where:  the dimensions are incompatible; or  the result is one of the arguments. ∕ , where the matrix is not square. scalar/matrix ÷ , where the matrix is not square. ÷ , where:  the matrix in the X-register is n...

209 Appendix B Stack Lift and the LAST X Register The HP-15C calculator has been designed to operate in a natural manner. As you have seen working through this handbook, most calculations do not require you to think about the operation of the automatic memory stack. There are occasions, however – es...

210 Appendix B: Stack Lift and the LAST X Register Disabling Operations Stack Lift. There are four stack-disabling operations on the calculator. * These operations disable the stack lift, so that a number keyed in after one of these disabling operations writes over the current number in the displaye...

Appendix B: Stack Lift and the LAST X Register 211 T y y y y Z x x x x Y 4.0000 53.1301 53.1301 53.1301 X 3 5.0000 0.0000 7 Keys: |: |` 7 Stack enabled. Stack disabled. No stack lift. Imaginary X-Register. All enabling functions provide for a zero to be placed in the imaginary X-register when the ne...

212 Appendix B: Stack Lift and the LAST X Register LAST X Register The following operations save x in the LAST X register: - x H \ k + [ H ] ∆ * \ h : ÷ ] À ; a , d p * q { r c * ‘ / N z & P[ ' w ∕ P\ o j ! P] @ > 5 through 9 ¤ H[ Y f † * Except when used as a matrix function. † f uses the LA...

213 Appendix C Memory Allocation The Memory Space Storage registers, program lines, and advanced function execution * all draw on a common memory space in the HP-15C. The availability of memory for a specific purpose depends on the current allocation of memory, as well as on the total memory capacit...

214 Appendix C: Memory Allocation Total allocatable memory: 64 registers, numbered R 2 through R 65 . [( dd – 1) + uu + pp + (matrix elements) + (imaginary stack) + ( _ and f )] = 64. For memory allocation and indirect addressing, data registers R .0 through R .9 are referred to as R 10 through R 19...

Appendix C: Memory Allocation 215 Memory Status ( W ) To view the current memory configuration of the calculator, press | W ( memory ), holding W to retain the display. * The display will be four numbers, dd uu pp-b where: dd = the number of the highest-numbered register in the data storage pool (ma...

216 Appendix C: Memory Allocation 1. Place dd , the number of the highest data storage register you want allocated, into the display. 1  dd  65. The number of registers in the uncommitted pool (and therefore potentially available for programming) will be (65 – dd ). 2. Press ´ m % . There are two ...

Appendix C: Memory Allocation 217 When converting registers, note that:  You can convert registers from the common pool only if they are uncommitted . If, for example, you try to convert registers which contain program instructions, you will get an Error 10 (insufficient memory).  You can convert ...

218 Appendix C: Memory Allocation Your very first program instruction will commit R 65 (all seven bytes) from an uncommitted register to a program register. Your eighth program instruction commits R 64 , and so on, until the boundary of the common pool is encountered. Registers from the data storage...

220 Appendix D A Detailed Look at _ Section 13, Finding the Roots of an Equation, includes the basic information needed for the effective use of the _ algorithm. This appendix presents more advanced, supplemental considerations regarding _ . How _ Works You will be able to use _ most effectively by ...

222 Appendix D: A Detailed Look at _  The function's graph is either convex everywhere or concave everywhere.  The only local minima and maxima of the function's graph occur singly between adjacent zeros of the function. In addition, it is assumed that the _ algorithm will not be interrupted by an...

224 Appendix D: A Detailed Look at _ the root 1.0000 is found for initial estimates of 1 and 2. By recognizing situations in which round-off error may influence the operation of _ , you can evaluate the results accordingly and perhaps rewrite the function to reduce the effects of round-off. In a var...

226 Appendix D: A Detailed Look at _ Execute _ again: Keystrokes Display | ¥ Run mode. 0 v 0.0000 Initial estimates. 1 1 ´ v B 4.0681 The desired root. ) 4.0681 A previous estimate of the root. ) 0.0000 Value of modified f(t) at root. After 4.0681 seconds, the ridget is at a height of 107 ± 0.5 mete...

228 Appendix D: A Detailed Look at _ Solution: The equation for the shear stress for x between 0 and 10 is more efficiently programmed after rewriting it using Horner's method: Q = (3 x –45) x 2 + 350 for 0 < x < 10. Keystrokes Display | ¥ 000– Program mode. ´ b 2 001–42,21, 2 1 002– 1 Test fo...

Appendix D: A Detailed Look at _ 229 Keystrokes Display | ¥ Run mode. 7 v 7.0000 Initial estimates. 14 14 ´_ 2 10.0000 Possible root. )) 1,000.0000 Stress not zero. The large stress value at the root points out that the _ routine has found a discontinuity. This is a place on the beam where the stres...

232 Appendix D: A Detailed Look at _ Keystrokes Display ÷ 017– 10 . 10 / x  ' 018– 12 + 019– 40 x e x e x e    2 2 1 0 / . 3 020– 3 + 021– 40 x e x e x e     2 2 1 0 / 3 . |n 022– 43 32 Use _ with the following single initial estimates: 10, 1, and 10 -20 . Keystrokes Display |¥ Run mode. 10 ...

Appendix D: A Detailed Look at _ 233 Keystrokes Display ´ _ .0 Error 8 − 1.0000 –20 Best x -value. ) 1.1250 –20 Previous value. ) 2.0000 Function value. | (| ( 1.0000 –20 Restore the stack. ´ _ .0 Error 8 − 1.1250 –20 Another x -value. ) 1.5626 –16 Previous value. ) 2.0000 Same function value. In ea...

234 Appendix D: A Detailed Look at _ add a few program lines at the end of your function subroutine. These lines should subtract the known root (to 10 significant digits) from the x -value and divide this difference into the function value. In many cases the root will be a simple one, and the new fu...

Appendix D: A Detailed Look at _ 235 Keystrokes Display - 008– 30 * 009– 20 3 010– 3 0 011– 0 0 012– 0 3 013– 3 + 014– 40 * 015– 20 6 016– 6 1 017– 1 7 018– 7 1 019– 1 + 020– 40 * 021– 20 2 022– 2 8 023– 8 9 024– 9 0 025– 0 - 026– 30 |n 027– 43 32 In Run mode, key in two large, negative initial esti...

236 Appendix D: A Detailed Look at _ Return to Program mode and add instructions to your subroutine to eliminate the root just found. Keystrokes Display |¥ 000- Program mode. | ‚ | ‚ 026– 30 Line before n . ® 027– 34 Brings x into X-register. l 0 028– 45 0 Divides by (x – a ), where a is known root....

238 Appendix D: A Detailed Look at _ Using the same initial estimates each time, you have found four roots for this equation involving a fourth-degree polynomial. However, the last two roots are quite close to each other and are actually one root (with a multiplicity of 2). That is why the root was ...

Appendix D: A Detailed Look at _ 239 Counting Iterations While searching for a root, _ typically samples your function at least a dozen times. Occasionally, _ may need to sample it one hundred times or more. (However, _ will always stop by itself.) Because your function subroutine is executed once f...

240 Appendix E A Detailed Look at f Section 14, Numerical Integration, presented the basic information you need to use f This appendix discusses more intricate aspects of f that are of interest if you use f often. How f Works The f algorithm calculates the integral of a function f(x) by computing a ...

Appendix E: A Detailed Look at f 241 The uncertainty of the final approximation is a number derived from the display format, which specifies the uncertainty for the function. * At the end of each iteration, the algorithm compares the approximation calculated during that iteration with the approximat...

242 Appendix E: A Detailed Look at f Calculate the integral in the expression for J 4 (1),       0 ) si n 4 cos( d First, switch to Program mode and key in a subroutine that evaluates the function f(θ) = cos (4 θ – sin θ ). Keystrokes Display |¥ 000- Program mode. ´ CLEAR M 000- ´ b 0 001–42,2...

244 Appendix E: A Detailed Look at f All 10 digits of the approximations in i 2 and i 3 are identical: the accuracy of the approximation in i 3 is no better than the accuracy in i 2 despite the fact that the uncertainty in i 3 is less than the uncertainty in i 2. Why is this? Remember that the accur...

Appendix E: A Detailed Look at f 245 This approximation took about twice as long as the approximation in i 3 or i 2. In this case, the algorithm had to evaluate the function at about twice as many sample points as before in order to achieve an approximation of acceptable accuracy. Note, however, tha...

246 Appendix E: A Detailed Look at f ) ( δ ) ( ) ( 2 x x f x F   , where δ 2 ( x ) is the uncertainty associated with f(x) that is caused by the approximation to the actual physical situation. Since ) ( δ ) ( ˆ ) ( 1 x x f x f   , the function you want to integrate is ) ( δ ) ( δ ) ( ˆ ) ( 2 1 x...

248 Appendix E: A Detailed Look at f   b a d x x ) δ ( Δ dx b a x m n ] 10 [0.5 ) (      . This integral is calculated using the samples of δ ( x ) in roughly the same ways that the approximation to the integral of the function is calculated using the samples of ) ( ˆ x f . Because Δ is propo...

Appendix E: A Detailed Look at f 249 Conditions That Could Cause Incorrect Results Although the f algorithm in the HP-15C is one of the best available, in certain situations it – like nearly all algorithms for numerical integration – might give you an incorrect answer. The possibility of this occurr...

Appendix E: A Detailed Look at f 251 Since you’re evaluating this integral numerically, you might think (naively in this case, as you'll see) that you should represent the upper limit of integration by 10 99 – which is virtually the largest number you can key into the calculator. Try it and see what...

252 Appendix E: A Detailed Look at f The graph is a spike very close to the origin. (Actually, to illustrate f(x) the width of the spike has been considerably exaggerated. Sho wn in actual scale over the interval of integration, the spike would be indistinguishable from the vertical axis of the grap...

254 Appendix E: A Detailed Look at f In many cases you will be familiar enough with the function you want to integrate that you’ll know whether the function has any quick wiggles relative to the interval of integration. If you're not familiar with the function, and you have reason to suspect that it...

Appendix E: A Detailed Look at f 255 Keystrokes Display 0 v 0.000 00 Keys lower limit into Y-register. ‛ 3 1 03 Keys upper limit into X-register. ´ f 1 1.000 00 Approximation to integral. ® 1.824 -04 Uncertainty of approximation. This is the correct answer, but it took almost 60 seconds. To understa...

258 Appendix E: A Detailed Look at f  If any other program line is displayed, return to Run mode and single-step (  ) through the program until you reach a n instruction (keycode 43 32) or line 000 (if there is no n ). (Be sure to hold the  key down long enough to view the program line numbers an...

259 Appendix F Batteries Batteries The HP-15C is shipped with two 3 Volt CR2032 Lithium batteries. Battery life depends on how the calculator is used. If the calculator is being used to perform operations other than running programs, it uses much less power. Low-Power Indication A battery symbol ( ...

Appendix F: Batteries 261 Verifying Proper Operation (Self-Tests) If it appears that the calculator will not turn on or otherwise is not operating properly, use the following procedures to access the test system; 1) Turn the calculator off. 2) Press and HOLD the | and v keys (keep both keys held dow...

262 Function Summary and Index = Turns the calculator's display on and off (page 18) . It is also used in resetting Continuous Memory (page 63) , changing the digit separator (page 61) , and in various tests of the calculator's operation (pages 261) . Complex Functions } Real exchange imaginary. Act...

264 Function Summary and Index number in display (X-register) (enter y, then x ). Causes the stack to drop (page 29) . Mathematics -+-÷ Arithmetic operators; cause the stack to drop (page 29) . ¤ Computes square root x (page 25) . x Computes the square of x (page 25) . ! Calculates the factorial ( n...

Function Summary and Index 265 matrices or of one matrix and a scalar. Stores in result matrix (page 152-155) . ÷ For two matrices, multiplies inverse of matrix in X by matrix in Y. For only one matrix, if matrix in Y, divides all elements of matrix by scalar in X; if matrix in X, multiplies each el...

266 Function Summary and Index register) by truncating fractional portion (page 24) . & Rounds mantissa of entire (10-digit) number in X-register to match display format (page 24) . Percentage k Percent. Computes x % (value in display) of number in the Y-register (page 29) . Unlike most two-numb...

Function Summary and Index 267 ` Clears contents of display (X-register) to zero (page 21) . − In Run mode: removes the last digit keyed in, or clears the display (if digit entry has been terminated) (page21) . Statistics z Accumulates numbers from X- and Y-registers into storage registers R 2 throu...

268 Function Summary and Index Trigonometry D Sets decimal Degrees mode for trigonometric functions—indicated by absence of GRAD or RAD annunciator (page 26) . Not operative for complex trigonometry. R Sets Radians mode for trigonometric functions—indicated by RAD annunciator (page 26) . g Sets Grad...

269 Programming Summary and Index ¥ Program/Run mode. Sets the calculator to Program mode ( PRGM annunciator on) or Run mode ( PRGM annunciator cleared) (page 66) . W Displays current status of calculator memory (number of registers dedicated to data storage, the common pool, and program memory) (pa...

271 Subject Index Page numbers in bold type indicate primary references; page numbers in regular type indicate secondary references. A ___________________________________________ Abbreviated key sequences, 78 Absolute value ( a ), 24 Allocating memory, 42, 213-219 Altering program lines, 83 Annuncia...

284 Product Regulatory & Environment Information Federal Communications Commission Notice This equipment 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 harm...

Declaration of Conformity for Products Marked with FCC Logo, United States Only This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions: (1) this device may not cause harmful interference, and (2) this device must accept any interference received, inc...

286 European Union Regulatory Notice Products bearing the CE marking comply with the following EU Directives: • Low Voltage Directive 2006/95/EC • EMC Directive 2004/108/EC • Ecodesign Directive 2009/125/EC, where applicable CE compliance of this product is valid if powered with the correct CE-marke...