HP 33s hp 33s_user's manual_English_E_HDPM20PIE56.pdf
HP 33s - Scientific Calculator Manual
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- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 1
hp 33s scientific calculator user's guide H Edition 3 HP part number F2216-90001 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 2
Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 3
Contents Part 1. Basic Operation 1. Getting Started Important Preliminaries 1-1 Turning the Calculator On and Off 1-1 Adjusting Display Contrast 1-1 Highlights of the Keyboard and Display 1-2 Shifted Keys 1-2 Alpha Keys 1-3 Cursor Keys 1-3 Silver Paint Keys 1-4 Backspacing and Clearing 1-4 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 4
and Commas in Numbers 1-18 Number of Decimal Places 1-19 SHOWing Full 12-Digit Precision 1-20 Fractions 1-21 Entering Fractions 1-21 Displaying Fractions 1-23 Messages 1-23 Calculator Memory 1-24 Checking Available Memory 1-24 Clearing All of Memory 1-24 2. RPN: The Automatic Memory - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 5
Entering 4-3 Setting the Angular Mode 4-4 Trigonometric Functions 4-4 Hyperbolic Functions 4-6 Percentage Functions 4-6 Physics Constants 4-8 Conversion Functions 4-9 Coordinate Conversions 4-10 Time Conversions 4-12 Angle Conversions 4-13 Unit Conversions 4-13 Probability Functions 4-14 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 6
in the Display 5-2 Display Rules 5-2 Accuracy Indicators 5-3 Longer Fractions 5-4 Changing the Fraction Display 5-4 Setting the Maximum Denominator 5-5 Choosing a Fraction Format 5-5 Examples of Fraction Displays 5-6 Rounding Fractions 5-7 Fractions in Equations 5-8 Fractions in Programs - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 7
Functions 6-15 Syntax Errors 6-18 Verifying Equations 6-18 7. Solving Equations Solving an Equation 7-1 Understanding and Controlling SOLVE 7-5 Verifying the Result 7-6 Interrupting a SOLVE Calculation 7-7 Choosing Initial Guesses for SOLVE 7-7 For More Information 7-11 8. Integrating - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 8
Using Complex Numbers in Polar Notation 9-5 10. Base Conversions and Arithmetic Arithmetic in Bases 2, 8, and 16 10 Errors in Data Entry 11-2 Statistical Calculations 11-4 Mean 11-4 Sample Standard Deviation 11-6 Population Standard Deviation 11-6 Linear Regression 11-7 Limitations on - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 9
and RTN 12-3 Using RPN, ALG and Equations in Programs 12-4 Data Input and Output 12-4 Entering a Program 12-5 Keys That Clear 12-6 Function Names in Programs 12-7 Running a Program 12-9 Executing a Program (XEQ 12-9 Testing a Program 12-9 Entering and Displaying Data 12-11 Using INPUT for - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 10
Addressing Variables and Labels 13-20 The Variable "i 13-20 The Indirect Address, (i 13-21 Program Control with (i 13-22 Equations with (i 13-24 14. Solving and Integrating Programs Solving a Program 14-1 Using SOLVE in a Program 14-6 Integrating a Program 14-7 Using Integration in - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 11
Standard Deviation 16-17 17. Miscellaneous Programs and Equations Time Value of Money 17-1 Prime Number Generator 17-6 Part 3. Appendixes and Reference A. Support, Batteries, and Service Calculator Support A-1 Answers to Common Questions A-1 Environmental Limits A-2 Changing the Batteries - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 12
C-4 Parentheses Calculations C-5 Chain Calculations C-5 Reviewing the Stack C-6 Coordinate Conversions C-7 Integrating an Equation C-8 Operations with Complex Numbers C-9 Arithmetic in Bases 2, 8, and 16 C-11 Entering Statistical Two-Variable Data C-12 D. More about Solving How SOLVE Finds - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 13
Underflow D-14 E. More about Integration How the Integral Is Evaluated E-1 Conditions That Could Cause Incorrect Results E-2 Conditions That Prolong Calculation Time E-7 F. Messages G. Operation Index Index Contents 11 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 14
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 15
Basic Operation Part 1 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 16
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 17
stored. To conserve energy, the calculator turns itself off after 10 minutes of no use. If you see the low-power 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 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 18
on its face, a left-shifted function (Green), and a right-shifted function (Purple). The shifted function names are printed in green and purple above each key. Press the appropriate shift key ({ or |) before pressing the key for the desired function. For example, to turn the calculator off, press - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 19
key Most keys have a letter written next to them, as shown above. Whenever you need to type a letter (for example, a variable or a program label), the A..Z annunciator appears in the display, indicating that the alpha keys are "active". Variables are covered in chapter 3; labels are covered in - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 20
the desired function. Backspacing and Clearing One of the first things you need to know is how to clear: how to correct numbers, clear the display, or start over. 1-4 Getting Started - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 21
is complete. b also clears error messages, and deletes the current program line during program entry. Clear or Cancel. Clears the displayed number to zero or cancels the current situation (such as a menu, a message, a prompt, a catalog, or Equation-entry or Program-entry mode). Getting Started 1-5 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 22
in memory. During program entry, {} is replaced by { }. If you select { }, a new menu is displayed, so you can verify your decision before erasing all your programs. During equation entry (either keyboard equations or equations in program lines), the menu is displayed, so you can - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 23
functions. HP 33s Menus standard deviation, population standard deviation. Functions to use 40 physics constants-refer to 4 " Physics constants" on page 4-8. Q 11 Statistical data summations. 11 Base conversions (decimal, hexadecimal, octal, and binary). Programming Instructions - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 24
R µ CLEAR HP 33s Menus (continued) Menu Description Chapter Other functions # Memory status (bytes of memory available); catalog of variables; catalog of programs (program labels). 1, 3, 12 8 Angular modes and ")" or "8" radix (decimal point) convention. 4, 1 1 Fix, scientific - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 25
7 = 0.8571428571... Keys: Display: 6 ‘ 7 q ({}) ( or š — ‘ ) % ) . Menus help you execute dozens of functions by guiding you to them with menu choices. You don't have to remember the names of the functions built into the calculator nor search through the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 26
enter the first number, press ›, enter the second number, and finally press the ‘ key. RPN mode 1 ‘2 › ALG mode 1›2‘ In ALG mode, the results and the calculations are displayed. In RPN mode, only the results are displayed, not the calculations. Note You can choose either ALG (Algebraic) or - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 27
more than 255 characters, the characters from the 256th onward are replaced with an ellipsis ()))). During inputting, the second line displays an entry; after calculating, it displays the result of a calculation. Every calculation is displayed in up to 14 digits, including an sign (exponent), and - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 28
Annunciator £ c d ¡ ¢ RPN ALG PRGM EQN 0 1 2 3 4 RAD or GRAD HEX OCT BIN HP 33s Annunciators Meaning Chapter The "£ (Busy)" annunciator blinks while an operation, equation, or program is executing. When in Fraction-display mode (press { 5 ‹), only one of the "c" or "d" halves of the "cd - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 29
HP 33s Annunciators (continued) Annunciator §,¨ Meaning Chapter The ˜ or — keys are active to scroll the 1, 6 display, i.e. there are more digits to the left and right. (Equation-entry and Program-entry mode aren't included) Use | to see the rest of a decimal number; use the left and right- - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 30
in a negative number, type the number, then press ^. „ To change the sign of a number that was entered previously, just press ^. (If the number has an exponent, ^ affects only the mantissa - the non-exponent part of the number.) Exponents of Ten Exponents in the Display Numbers with exponents - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 31
power of ten without a multiplier, such as 1034, just press a 34. The calculator displays . Other Exponent Functions To calculate an exponent of ten (the base 10 antilogarithm), use { . To calculate the result of any number raised to a power (exponentiation), use (see chapter 4). Understanding - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 32
. Try it! Range of Numbers and OVERFLOW The smallest number available on the calculator is 1 × 10-499. The largest number is 9.99999999999 × 10499 (displayed as ) because of rounding). „ If a calculation produces a result that exceeds the largest possible number, 9.99999999999 × 10499 is - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 33
.) For example, calculate 1/32 and 148.84 . Then square the last result and change its sign. Keys: Display: Description: 32 second. 3. Key in the second number. (Do not press ‘.) 4. Press the function key. (For a shifted function, press the appropriate shift key first.) Note In RPN mode, type - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 34
calculate: 12 + 3 12 - 3 12 × 3 123 Percent change from 8 to 5 Press: 12 ‘ 3 › 12 ‘ 3 … 12 ‘ 3 z 12 ‘ 3 8‘5|T Display: 8 ) . ) The order of entry is important only for non-commutative functions such as …, q, , { F, | D Q, | T. If you type Press Ÿ to display the MODES menu. 2. - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 35
you see when the calculator is set to FIX 4 display mode. Any number that is too large or too small to display in the current decimal-place setting will automatically be displayed in scientific format. Scientific Format ({ }) SCI format displays a number in scientific notation (one digit before - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 36
digits before the ")" or "8" radix mark). This format is most useful for scientific and engineering calculations that use units specified in multiples of 103 (such as micro-, milli-, and kilo-units.) After the prompt, _, type in the number of digits you want after the first significant digit. For - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 37
. Four decimal places displayed. Scientific format: two decimal places and an exponent. Engineering format. All significant digits; trailing zeros dropped. Four decimal places, no exponent. Reciprocal of 58.5. Shows full precision until you release Fractions The HP 33s allows you to type in and - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 38
fraction (the number is still displayed in decimal form). The calculator interprets the second as a fraction and Display: Description: 3 8 ‘ + _ ) Enters no integer part. (3 8 also works.) Terminates digit entry; displays the number in the current display format (FIX 4). 1-22 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 39
{‹ to switch between Fraction-display mode and the current decimal display mode. Keys: Display: Description: 12 3 8 ‘ {‹ + Displays characters as you key them in. Terminates digit entry; displays the number in the current display format. Displays the number as a fraction - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 40
Calculator Memory The HP 33s has 31KB of memory in which you can store any combination of data (variables, equations, or program lines). Checking Available Memory Pressing { Y displays the following menu: 8 Where 8 is the number of bytes of memory available. Pressing the {# } menu key - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 41
you will learn how the stack can help you to manipulate and organize data for programs. What the Stack Is Automatic storage of intermediate results is the reason that the HP 33s easily processes complex calculations, and does so without parentheses. The key to automatic storage is the automatic, RPN - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 42
second line of the display. In programming, the stack is used to perform calculations, to temporarily store intermediate results, to pass stored data (variables) among programs to program this instruction. The ‡ key, in contrast, is context-sensitive. It either clears or cancels the current display, - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 43
(Roll Down) The (roll down) key lets you review the entire contents of the stack by "rolling" the contents are rolled - the registers themselves maintain their positions, and only the X- and Y-register's contents are displayed. Rµ (Roll Up) The | (roll up) key has a similar function to stack - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 44
(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 1. The stack "drops" its contents. The T-(top) register replicates its contents. 2. The stack "lifts" its contents. The T-register's contents are lost - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 45
drops. „ Notice that when the stack lifts, it replaces the contents of the T- (top) register with the contents movements of the stack, you do not need to clear the X-register before doing a new calculation. „ Most functions prepare the stack to lift its contents when the next number enters the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 46
(from T into Z) allows you to fill the stack with a numeric constant for calculations. Example: Given bacterial culture with a constant growth rate of 50% per day, how ‡ 2. Press b 3. Press { c {º} (Mainly used during program entry.) Note these exceptions: 2-6 RPN: The Automatic Memory Stack - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 47
displayed program line and ‡ cancels program entry. „ During digit entry, b backspaces over the displayed number. „ If the display shows a labeled number (such as /) ), pressing ‡ or b cancels that display and shows the X-register. „ When viewing an equation, b displays x (replaces the zero - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 48
2. Reusing a number in a calculation. See appendix B for a comprehensive list of the functions that 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 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 49
number{ q 19 z Reusing Numbers with LAST X You can use { to reuse a number (such as a constant) in a calculation. Remember to enter the constant second, just before executing the arithmetic operation, so that the constant is the last number in the X-register, and therefore can be saved and - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 50
.3947 t t z 2. 8 457 52.3947 t t z 149.0987 52.3947 Keys: 96.704 ‘ 52.3947 › { q Display: ) ) ) ) Description: Enters first number. Intermediate result. Brings back display from before ›. Final result. Example: Two close stellar neighbors of Earth are Rigel Centaurus - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 51
(12 + 3) = 1 5 ... then you would multiply the intermediate result by 7: (15) × 7 = 105 Solve the problem in the same way on the HP 33s, starting inside the parentheses: Keys: Display: Description: 12 ‘ 3 › ) Calculates the intermediate result first. You don't need to press ‘ to save - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 52
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 33s, except that you don - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 53
- 12) × 4] = 0.2500 Solution: 17 ‘ 12 … 4 z 10 ‘ 5 … [ q or 10 ‘ 5 … 17 ‘ 12 … 4 z q 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 left-to-right order. For example, you have already - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 54
above example, when solved left-to-right, needed all registers in the stack at one point: Keys: Display: Description: 4 calculation. Intermediate result. Intermediate result. Intermediate result. Final result. More Exercises Practice using RPN by working through the following problems: Calculate - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 55
: 232 - (13 × 9) + 1/7 = 412.1429 A Solution: 23 ! 13 ‘ 9 z … 7 › Calculate: (5.4 × 0.8) ÷ (12.5 − 0.73) = 0.5961 Solution: 5.4 ‘ .8 z .7 ‘ 3 12.5 [ … q# or 5.4 ‘ .8 z 12.5 ‘ .7 ‘ 3 … q # Calculate: 8.33× (4 − 5.2) ÷ [(8.33 − 7.46) × 0.32] = 4.5728 4.3× (3.15 − 2.75) − (1.71× 2.01) A Solution - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 56
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 57
3 Storing Data into Variables The HP 33s has 31KB of user memory: memory that you can use to store numbers, equations, and program lines. Numbers are stored in locations called variables, each named with a letter from A through Z. (You can choose the letter to remind you of what is - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 58
letter is associated with a key and a unique variable. The letter keys are automatically active when needed. (The A..Z annunciator in the display confirms this.) Note that the variables, X, Y, Z and T are different storage locations from the X-register, Y-register, Z-register, and T-register in the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 59
{ } menu key displays the catalog of programs. To review the values at any or all non-zero variables: 1. Press { Y {VAR}. 2. Press š or ™ to move the list and display the desired variable. (Note the ©ª annunciators, indicating that the š and ™ keys are active. If Fraction-display mode is active - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 60
Press { Y {# } and use š or ™ to display the variable. 2. Press { c. 3. Press ‡ to cancel the catalog. To clear all variables at once: Press { c {# }. Arithmetic with Stored Variables Storage arithmetic and recall arithmetic allow you to do calculations with a number stored in a variable without - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 61
you want to divide the number in the X-register (3, displayed) by the value in A(12). Press L q A. Now x = 0.25, while 12 is still in A. Recall arithmetic saves memory in programs: using L › A (one instruction) uses half as much memory as L A, › (two instructions). A 12 A 12 Tt Zz Yy X3 Tt Zz Yy - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 62
F contain the values 2, 3, and 4 from the last example. Divide 3 by D, multiply it by E, and add F to the result. Keys: Display: Description: 3LqD LzE L›F Calculates 3 ÷ D. 3 ÷ D × E. 3 ÷ D × E + F. Exchanging x with Any Variable The | Z key allows you to exchange the contents of x (the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 63
, i is special in that it can be used to refer to other variables, including the statistics registers, using the (i) function. This is a programming technique called indirect addressing that is covered under "Indirectly Addressing Variables and Labels" in chapter 13. Storing Data into Variables 3-7 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 64
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 65
of the calculator's functions that perform computations on real numbers, including some numeric functions used in programs (such as Conversion functions for coordinates, angles, and units. „ Probability functions. „ Parts of numbers (number-altering functions). Arithmetic functions and calculations - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 66
Key in the second number. (Do not press ‘.) 4. Press the function key. Example: To display the quotient and remainder produced by 58 ÷ 9 Keys: Display: Description: 58 ‘ 9 { F ) 58 ‘ 9 | D ) Displays the quotient. Displays the remainder. Power Functions To calculate the square of - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 67
125 ^ { @ Result: ) 8 8 ) ) ) .) In RPN mode, to calculate a root x of a number y (the xth root of y), key in y ‘ x, displayed depends on the display format.) Because π is a function, it doesn't need to be separated from another number by ‘. Note that the calculator - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 68
. Option Description Annunciator {} { } { } Sets Degrees mode (DEG). Uses decimal degrees, not degrees, minutes, and seconds. Sets Radians mode (RAD). Sets Grads mode (GRAD). none RAD GRAD Trigonometric Functions With x in the display: To Calculate: Press: Sine of x. O Note - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 69
Keys: Display: Description: Ÿ { } 5 7 ‘ |NzR Ÿ {} 128.57 R ) . ) Sets Radians mode; RAD annunciator on. 5/7 in decimal format. Cos (5/7)π. Switches to Degrees mode (no annunciator). Calculates cos 128.57°, which is the same as cos (5/7)π. Programming Note: Equations using - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 70
both the base number and the result without reentering the base number. To Calculate: x% of y Percentage change from y to x. (y≠ 0) Press: y‘xQ y‘x|T Example: Find the sales tax at 6% and the total cost of a $15.76 item. Use FIX 2 display format so the costs are rounded appropriately. Keys - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 71
(base price + 6% tax). Suppose that the $15.76 item cost $16.12 last year. What is the percentage change from last year's price to this year's? Keys: Display: Description: 16.12 ‘ 15.76 | T {%} 4 .) This year's price dropped about 2.2% from last year's price. Restores FIX 4 format - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 72
items. CONST Menu Items {F} {J} {} {#P H} {PH} {PR} {PQ} {P_} {N} {K} {K} {«µ} {Dµ} {εµ} {} {} {W H} {WQ} {__} Description Speed of light in vacuum Standard acceleration of gravity Newtonian constant of gravitation Molar volume of ideal gas Avogadro constant Rydberg constant Elementary charge - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 73
Standard atmosphere Proton gyromagnetic ratio First radiation constant Second . 2. Press | ž to display the physics constants menu. 3. Press Conversion Functions There are four types of conversions: coordinate (polar/rectangular), angular (degrees/radians), time (decimal/minutes-seconds), and unit - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 74
The function names for these conversions are y,xÆθ,r and θ,rÆy,x. Polar coordinates (r,θ) and rectangular coordinates (x,y) are measured as shown in the illustration. The angle θ uses units set by the current angular mode. A calculated result for θ will be between -180° and 180°, between -π and - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 75
r and angle θ in the triangle on the right. 10 30o x y r 4 θ 3 Keys: Display: Ÿ {} 30 ‘ 10 | s [ 4‘3{r [ Description: Sets Degrees mode. Calculates x. Displays y. Calculates hypotenuse (r). Displays θ. Example: Conversion with Vectors. Engineer P.C. Bord has determined that in the RC - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 76
and dot product), refer to the "Vector Operations" program in chapter 15, "Mathematics Programs". Time Conversions Values for time (in hours, H) or angles (in degrees, D) can be converted between a decimal-fraction form (H.h or D.d) and a minutes-seconds form (H.MMSSss or D.MMSSss) using the { t or - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 77
to be radians. To convert an angle between degrees and radians: 1. Key in the angle (in decimal degrees or radians) that you want to convert. 2. Press | w or { v. The result is displayed. Unit Conversions The HP 33s has eight unit-conversion functions on the keyboard: €kg, €lb, €ºC, €ºF, €cm, €in - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 78
calculate the factorial of a displayed non-negative integer x (0 ≤ x ≤ 253), press { (the left-shifted key). Gamma To calculate the gamma function of a noninteger x, Γ(x), key in (x - 1) and press { . The x! function calculates The Art of Computer Programming, vol. 2, Seminumerical Algorithms, London: - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 79
seed is reset to zero. A seed of zero will result in the calculator generating its own seed. Example: Combinations of People. A company employing 14 women number of combinations for that event by the total number of combinations. Keys: Display: Description: 14 ‘ 6 {\ [ q _ 8 8 ) ) - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 80
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 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 81
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 O, the display shows . "SIN" is the name of the function as it will appear in program lines (and usually in equations also). Real-Number Functions 4-17 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 82
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 83
basics about entering, displaying, and calculating with fractions: „ To enter a fraction, press twice - after the integer part, and between the numerator and denominator. To enter 2 3/8, press 2 3 8. To enter 5/8, press 5 8 or 5 8. „ To turn Fraction-display mode on and off, press - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 84
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 In Fraction-display mode, numbers are evaluated internally as decimal numbers, then - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 85
fraction is indicated by the c and d annunciators at the right of the display. The calculator compares the value of the fractional part of the internal 12-digit number with the value of the displayed fraction: „ If no indicator is lit, the fractional part of the internal 12-digit value exactly - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 86
decimal digits. Stores value in A. Views A. Clears x. Changing the Fraction Display In its default condition, the calculator displays a fractional number according to certain rules. (See "Display Rules" earlier in this chapter.) However, you can change the rules according to how you want fractions - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 87
4095 or greater.) This also turns on Fraction-display mode. The /c function uses the absolute value of the integer part of the number in the X-register. It doesn't change the value in the LAST X register. Choosing a Fraction Format The calculator has three fraction formats. Regardless of the format - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 88
You can change flags 8 and 9 to set the fraction format using the steps listed here. (Because flags are especially useful in programs, their use type the flag number. Press ‡ or b to clear the & or response. Examples of Fraction Displays The following table shows how the number 2.77 is displayed - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 89
of denominator" format. Sets up fraction format for 1/8 increments. Enters the starting value. Subtracts the change. Finds the 85-percent value to the nearest 1/8. Rounding Fractions If Fraction-display mode is active, the RND function converts the number in the X-register to the closest decimal - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 90
equation or program, the RND function does fractional rounding if Fraction-display mode display mode. Fractions in Equations When you're typing an equation, you can't type a number as a fraction. When an equation is displayed, all numeric values are shown as decimal values - Fraction-display mode - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 91
as decimal values - Fraction-display mode is ignored. When you're running a program, displayed values are shown using Fraction-display mode if it's active. If you're prompted for values by INPUT instructions, you may enter fractions, regardless of the display mode. A program can control the fraction - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 92
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, you get the HP 33s to "remember" the relationship between diameter, length, and volume - so you can use it many times. Put the calculator in Equation mode and type in the equation using the following keystrokes: Keys: |H Display: Description: Selects Equation mode, shown or the current - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 94
restores the "¾" cursor. types :. Terminates and displays the equation. Shows the checksum and length for the equation, so you can check your equation properly. (See "Verifying Equations" at the end of this chapter for more information.) Evaluate the equation ( to calculate V ): Keys: Display - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 95
left-hand side. If the equation is an equality or expression, calculates its value like X. (See "Types of Equations" later in this chapter.) Evaluates the displayed equation. Calculates its value, replacing "=" with "-" if an "=" is present. Solves the displayed equation for the unknown variable you - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 96
the catalog of variables or programs. 2. Press | H. The EQN annunciator shows that Equation mode is active, and an entry from the equation list is displayed. 3. Start typing the equation. The previous display is replaced by the equation you're entering - the previous equation isn't affected. If you - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 97
you type one or more digits. Don't use ^ for subtraction. When you start entering the number, the cursor changes from "¾" to "_" to show numeric entry. The cursor changes back when you press a nonnumeric key. Functions in Equations You can enter many HP 33s functions in an equation. A complete - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 98
number, changing the cursor to "_". Enters infix operators. Enters a prefix function with a left parenthesis. Enters the argument and right parenthesis. Terminates the equation and displays it. Shows its checksum and length. Leaves Equation mode. Displaying and Selecting Equations The equation list - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 99
Displays the current equation in the equation list. Shows three more characters to the right. Shows one character to the left. Leaves Equation mode. Editing and Clearing Equations You can edit or clear an equation that you're typing. You can also edit or clear equations saved in the equation - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 100
to save the edited equation in the equation list, replacing the previous version. To clear an equation you're typing: Press { c then press {&}. The display goes back to the previous entry in the equation list. To clear a saved equation: 1. Display the desired equation. (See "Displaying and Selecting - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 101
equation in the equation list. Leaves Equation mode. Types of Equations The HP 33s works with three types of equations: „ Equalities. The equation calculating with an equation, you might use any type of equation - although the type can affect how it's evaluated. When you're solving a problem - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 102
is the difference between the values of the two sides. For this calculation, "=" in an equation essentially treated as "ಥ". The value is a measure of how well the equation balances. The HP 33s has two keys for evaluating equations: ‘ and X. Their actions differ only in how they evaluate assignment - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 103
of this chapter to find the volume of a 35-mm diameter pipe that's 20 meters long. Keys: Display: Description: |H ( ™ as required) ‘ 35 g 20 ‘ 1000 zg 88) Displays the desired equation. Starts evaluating the assignment equation so the value will be stored in V. Prompts - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 104
of the type of equation. The result is returned to the X-register. 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. Keys: Display: Description: |H X g 35 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 105
enter a number as a fraction if you want. If you need to calculate a number, use normal keyboard calculations, then press g. For example, you can press 2 ‘ 5 g. „ To calculate with the displayed number, press ‘ before typing another number. „ To cancel the prompt, press ‡. The current value for - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 106
, all operations inside parentheses are performed before operations outside the parentheses. Examples: Equations º:/ 1º2 1-2ª/ 01!-(. 2: Meaning a × (b3) = c (a × b)3 = c a + (b/c) = 12 (a + b) / c = 12 [%CHG ((t + 12), (a - 6)) ]2 You can't use parentheses for implied - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 107
Σy2 ATANH XROOT €IN y b Σxy For convenience, prefix-type functions, which require one or two arguments, display a left parenthesis when you enter them. The prefix functions that second argument is negative. For a number or variable, use ^ or …. These are valid equations: Entering and Evaluating - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 108
Perimeter of a Trapezoid. The following equation calculates the perimeter of a trapezoid. This is how the equation might appear in a book: 1 Perimeter = a + b + h ( sinθ + 1 sinφ ) a h θ φ b The following equation obeys the syntax rules for HP 33s equations: 6-16 Entering and Evaluating - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 109
form, ª 1!2. Notice that the SIN function is "nested" inside the INV function. (INV is typed by .) /--º1#1 1!22-#1 1222 Example: Area of a Polygon. The equation for area of a regular polygon with n sides of length d is: Area = 1 n d 2 cos(π / n) 4 sin(π/n) d 2π/n You - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 110
value is actually being calculated. If an error is detected is displayed. You have to edit the equation to correct the error. (See "Editing and Clearing Equations" earlier in this chapter.) By not checking equation syntax until evaluation, the HP 33s lets you create "equations" that might actually - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 111
know the value of y in this equation, then SOLVE can solve for the unknown x. If you know the value of x, then SOLVE can solve for the unknown y. This works for "word problems" just as well: Markup × Cost = Price If you know any two of these variables, then SOLVE can calculate the value of the third - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 112
, v0 is the initial velocity, t is the time, and g is the acceleration due to gravity. Type in the equation: Keys: Display: Description: { c {} {&} |H LD|dLV zLT› .5 z L G z L T 2 or current equation Clears memory. Selects Equation mode. Starts the equation. 7-2 Solving Equations - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 113
so you can change it for different units (9.8 m/s2 or 32.2 ft/s2 ). Calculate how many meters an object falls in 5 seconds, starting from rest. Since Equation mode is turned on and the desired equation is already in the display, you can start solving for D: Keys: Display: Description: D 0g 5g - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 114
24°C. Assuming that the gas behaves as an ideal gas, calculate its pressure. Since Equation mode is turned on and the desired equation is already in the display, you can start solving for P: Keys: Display: Description: P 2g .005 g .0821 g 24 ‘ 273.1› #@ value @ value @ value !@ value - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 115
T (Kelvins). Stores 291.1 in T; solves for N. Calculates mass in grams, N × 28. Calculates density in grams per liter. 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 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 116
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 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 117
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 solution, guesses can direct the SOLVE procedure to the desired answer or range of answers. For example, the equation of linear motion d = v0 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 118
+ 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 - 2H ) × (40 - 2H ) × H which you can simplify and enter as V= ( 40 - H ) × ( 20 - H ) × 4 × H 7-8 Solving Equations - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 119
wide. Initial estimates of 10 and 20 cm are therefore appropriate. Keys: Display: Description: ‡ 10 I H 20 |H H 7500 g Leaves Equation mode. Stores lower and upper limit _ guesses. #/1 .2º1 . Displays current equation. #@ Solves for H; prompts for V. value / Stores - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 120
the value of H to produce different values for the equation. Remember that the value for this equation is the difference between the left and right sides of the equation. The plot of the value of this equation looks like this. 7500 _ (40_H) (20_H) 4H 20,000 _10 _10,000 7-10 Solving Equations H 50 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 121
For More Information This chapter gives you instructions for solving for unknowns or roots over a wide range of applications. Appendix D contains more detailed information about how the algorithm for SOLVE works, how to interpret results, what happens when no solution is found, and conditions that - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 122
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 123
8 Integrating Equations Many problems in mathematics, science, and engineering require calculating the definite integral throughout the interval of integration). The operation ( ³ FN) integrates the current equation with respect to a specified variable ( ³ d_). The function may have more - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 124
Display the equation: Press | H and, if necessary, scroll through the equation list (press ™ or š) to display the desired equation. 4. Select the variable of integration: Press | variable. This starts the calculation problem using a different equation, start over from step 1 with an equation that - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 125
zO L T |`|` ‘ | ‡ Clears memory. Current equation or 1%¾ 1%º 1¾ 1%º 1!¾ 1%º 1!22¾ 1%º 1!22 Selects Equation mode. Types the equation. Terminates the expression and displays its left end. Checksum and length. Leaves Equation mode. Now integrate this function with - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 126
integration (lower limit first). Displays the current equation. Prompts for the variable of integration. Prompts for value of X. x = 3. Starts integrating and calculates the result for π ³ f (t) . 0 The final result for J0(3). Example: Sine Integral. Certain problems in communications theory (for - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 127
Display: Description: Ÿ { } 0‘2 |H | X _ 1%2 Selects Radians mode. Enters limits of integration (lower first). Displays the current equation. Calculates be calculated inaccurately, but the likelihood is very small. The general characteristics of functions that can cause problems, as - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 128
and precision will be reflected in the result of integration. If Fraction-display mode is on (flag 7 set), the accuracy is specified by the previous display format. Interpreting Accuracy After calculating the integral, the calculator places the estimated uncertainty of that integral's result in the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 129
accuracy to four decimal places. The uncertainty from the last example is still in the display. Rolls down the limits of integration from the Z- and T-registers into the X- and Y-registers. Displays the current equation. Calculates the result. Note that the uncertainty is about 1/100 as large as the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 130
. Since the uncertainty of a result is calculated conservatively, the calculator's approximation in most cases is more accurate than its uncertainty indicates. For More Information This chapter gives you instructions for using integration in the HP 33s over a wide range of applications. Appendix - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 131
complex number: 1. Type the imaginary part. 2. Press ‘. 3. Type the real part. Complex numbers in the HP 33s are handled by entering i 9. (The first line is the imaginary and the second is the real part.) The Complex Stack In RPN mode, the complex stack is really the regular memory stack split into - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 132
result, z Always enter the imaginary part (the y-part) of a number first. The real portion of the result (zx) is displayed on the second line; the imaginary portion (zy) is displayed on the first line. (For two-number operations, the first complex number, z1, is replicated in the stack's Z and - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 133
Functions for One Complex Number, z To Calculate: Change sign, -z Inverse, 1/z Natural log, ln z Natural antilog, ez Sin z z1z2 , key in the exponent, z2, second.) 3. Select the arithmetic operation: Arithmetic With Two Complex Numbers, z1 and z2 To Calculate: Addition, z1 + z2 Subtraction, z1 - - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 134
z2 + z3). z1 ÷ (z2 + z3). Result is 2.5 + i 9. Evaluate (4 - i 2/5) (3 - i 2/3). Do not use complex operations when calculating just one part of a complex number. Keys: Display: Description: 25^‘ 4‘ Enters imaginary part of first complex number as a fraction. Enters real part of first - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 135
second number and then multiplies the two complex numbers. Result is 11.7333 - i 3.8667. Evaluate ez −2 , where z = (1 + i ). Use { G to evaluate z-2; enter -2 as -2 + i 0. Keys: Display by using the complex operations. Since the HP 33s's complex operations work on numbers in rectangular - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 136
. y L2 185 lb 62 o 170 lb 143 o L1 x L3 100 lb 261 o Keys: Ÿ {} 62 ‘ 185 | s 143 ‘ 170 | s {G› 261 ‘ 100 | s Display: Description: Sets Degrees mode. Enters L1 and converts it to rectangular form. Enters and converts L2. Adds vectors. Enters and converts L3. 9-6 Operations with - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 137
{G› {r ) Adds L1 + L2 + L3. Converts vector back to polar form; displays r, θ Operations with Complex Numbers 9-7 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 138
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 139
operations (including programming). Changing bases also converts the displayed number to the new base. BASE Menu Menu label {} {%} { !} {} Description Decimal mode. No annunciator. Converts numbers to base 10. Numbers have integer and fractional parts. Hexadecimal mode. HEX annunciator on - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 140
the maximum display) long. Keys: Display: Description: { x {%} 24FF { x {} ˜ — { x {} 8 ) Use the ! key to type "F". The calculation. „ The result of an operation is always an integer (any fractional portion is truncated). Whereas conversions change only the displayed - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 141
Example: Here are some examples of arithmetic in Hexadecimal, Octal, and Binary modes: Keys: 12F16 + E9A16 = ? Display: Description: { x {%} 12F ‘ E9A › Sets base 16; HEX annunciator on. Result. { x { !} 7760 ‘ 4326 … 77608 - 43268 =? Sets base 8; OCT annunciator on - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 142
display of a number is converted when the base is changed, its stored form is not modified, so decimal numbers are not truncated - until they are used in arithmetic calculations 12510 is displayed as: 1111101 complement (sign changed). Binary version; § indicates more digits. Displays the leftmost - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 143
Range of Numbers for Base Conversions Base Hexadecimal Octal Binary Decimal modes. In RPN mode, the original decimal value of any too-big number is used in calculations. Any operation that results in a number outside the range given above causes OVERFLOW to be briefly displayed. The display - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 144
§ or ¨ annunciator (or both) appears, indicating in which direction the additional digits lie. Press the indicated key ( ˜ or — ) to view the obscured window. Press to display left window Press to display right window 10-6 Base Conversions and Arithmetic - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 145
the HP 33s provide functions to statistically analyze a set of one- or two-variable data: „ Mean, sample and population standard deviations. are accumulated as summation statistics in six statistics registers (28 through 33), whose names are displayed in the SUMS menu. (Press | and see Q Note - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 146
the Y-register is accumulated as the y-value. For this reason, the calculator will perform linear regression and show you values based on y even when To recall a value to the display immediately after it has been entered, press { . Entering Two-Variable Data In RPN mode, when your data consist of - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 147
y-values on the left, then make the corrections shown on the right: Initial x, y Corrected x, y 20, 4 400, 6 20, 5 40, 6 Keys: { c {´} 4 ‘ 20 6 ‘ 400 { { 6 ‘ 40 4 ‘ 20 { 5 ‘ 20 Display: Description: Clears existing statistical data. Enters the first new data pair - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 148
Statistical Calculations Once you have entered your data, you can use the menu See "Mean" below. The standard-deviation menu: {Uº} {U See "Sample Standard Deviation" and "Population Standard Deviation" later in this chapter. The summation time required (in minutes): 11-4 Statistical Operations - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 149
y, the weight (frequency), before x, the price. Keys: Display: Description: { c {´} 250 ‘ 4.25 800 ‘ 4.6 900 ‘ 4.7 1000 ‘4.1 | {º·} 8 ) Clears the statistics registers. Enters data; displays n. Four data pairs accumulated. Calculates the mean price weighted for the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 150
, May Kitt now wants to determine the standard deviation time (sx) of the process: 15.5 9.25 10.0 12.5 12.0 8.5 Calculate the standard deviation of the times. (Treat all the data as x-values.) Keys: Display: Description: { c {´} 15.5 9.25 10 12.5 12 8.5 | {Uº} Clears - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 151
. Find the population standard deviation of their heights. Keys: Display: Description: { c {´} 170 173 174 180 Clears the statistics registers. Enters data. Four data points ) accumulated. UºU Calculates the population ) standard deviation. Linear Regression - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 152
4.63 ‘ 0 5.78 ‘ 20 6.61 ‘ 40 7.21 ‘ 60 7.78 ‘ 80 | {T} — — Display: ) ) ºˆ ¸ˆ T P E ) ºˆ ¸ˆ T P E ) ºˆ ¸ˆ T PE ) Description: Clears all previous statistical data. Enters data; displays n. Five data pairs entered. Displays linear-regression menu - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 153
the grain yield based on the above statistics. Keys: Display: Description: ‡ 70 | { ¸ˆ } ) _ ºˆ ¸ˆ T P E ) Enters hypothetical x-value. The predicted yield in tons per hectare. Limitations on Precision of Data Since the calculator uses finite precision (12 to 15 digits), it - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 154
Close, Large Numbers The calculator might be unable to correctly calculate the standard deviation and linear regression for a y values have greatly different magnitudes. Again, scaling the data can avoid this problem. Effect of Deleted Data Executing { does not delete any rounding errors - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 155
Registers in Calculator Memory The memory space for the statistics registers is automatically allocated when you press or . The registers are deleted and the memory deallocated when you execute { c {´}. Access to the Statistics Registers The statistics register assignments in the HP 33s are - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 156
You can load a statistics register with a summation by storing the number (28 through 33) of the register you want in i (number I “) and then storing the , you can press | Š ” to view a register value - the display is labeled with the register name. The SUMS menu contains functions for recalling the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 157
Programming Part 2 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 158
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 159
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 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 160
following: Keys: (In RPN mode) Display: Description: { c {} {&} {e {V ! |N z {e ! Clears memory. Activates Program-entry mode (PRGM annunciator on). Resets program pointer to PRGM TOP. (Radius)2 Area = πx2 Exits Program-entry mode. Try running this program to find the area - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 161
be edited and executed in ALG mode. You can ensure that your program executes in the correct mode by making RPN or ALG the first instruction in the program. Program Boundaries (LBL and RTN) If you want more than one program stored in program memory, then a program needs a label to mark its beginning - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 162
to ‘ for an assignment equation - other than writing the equation as an expression, then using STO to store the value in a variable.) For both types of calculations, you can include RPN instructions to control input, output, and program flow. Data Input and Output For programs that need more than - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 163
written for ALG mode should normally have an "=" (ENTER) as the last instruction in the program (before the RTN instruction). This will complete any pending calculations and allow the user to re-use the result of the program in further calculations. To enter an equation in a program line, see the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 164
To enter an equation in a program line: 1. Press | H to activate Equation-entry mode. The EQN annunciator turns on. 2. Enter the equation as you would in the equation list. See chapter 6 for details. Use b to correct errors as you type. 3. Press ‘ to terminate the equation and display its left end - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 165
a label and a return instruction. If you make a mistake during entry, press b to delete the current program line, then reenter the line correctly. Keys: (In RPN mode) Display: Description: {e { c { } {&} {• A ! |N z |– { Y { } | ‡‡ Activates Program-entry mode (PRGM on). Clears - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 166
Example: Entering a Program with an Equation. The following program calculates the area of a circle using an equation, rather than using RPN operations like the previous program. Keys: (In RPN mode) Display: Description: {e{ V {• E I R ! | H | N zLR 2 ‘ | |– { Y - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 167
executing A or E. Keys: (In RPN mode) Display: Description: 5X A " ) 2.5 X E ) 2|NzX A ) Enters the radius, then starts program A. The resulting area is displayed. Calculates area of the second circle using program E. Calculates area of the third circle - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 168
the start of the program (that is, at its LBL instruction). The ! instruction moves the program pointer without starting execution. (If the program is the first or only program, you can press { V to move to its beginning.) 3. Press and hold š. This displays the current program line. When you - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 169
In a displayed equation (if enabled by flag 10 set). (The "equation" is usually a message, not a true equation.) Some of these input and output techniques are described in the following topics. Using INPUT for Entering Data The INPUT instruction ( { ‰ Variable ) stops a running program and displays - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 170
the given variable. If you have not changed the displayed value, then that value is retained in the X-register. The area-of-a-circle program with an INPUT instruction looks like this: RPN mode ALG mode ! To use the INPUT function in a program: 1. Decide which data values you will need - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 171
Using VIEW for Displaying Data The programmed VIEW instruction ( | Š variable ) stops a running program and displays and identifies the contents of the given variable, such as / ) This is a display only, and does not copy the number to the X-register. If Fraction-display mode is active, the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 172
also that this VIEW instruction in this program is preceded by a RCL instruction. The RCL instruction is not necessary, but it is convenient because it brings the VIEWed variable to the X-register, making it available for manual calculations. (Pressing ‘ while viewing a VIEW display would have the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 173
of memory. Labels program. Instructions to prompt for radius and height. Calculates the volume. Checksum and length of equation. Store the volume in V. Calculates the surface area. Checksum and length of equation. Stores the surface area in S. Sets flag 10 to display equations. Displays message in - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 174
If you want, you can make the program continue while the information is displayed. If the next program line - after a VIEW instruction or a viewed equation - contains a PSE (pause) instruction, the information is displayed and execution continues after a 1-second pause. In this case, no scrolling or - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 175
exception. If PSE immediately follows a VIEW instruction or an equation that's displayed (flag 10 set), the variable or equation is displayed instead - and the display remains after the 1-second pause. Interrupting a Running Program You can interrupt a running program at any time by pressing ‡ or - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 176
you want to change - if it contains an equation, press { c { }; otherwise, press b. The pointer then moves to the preceding line. (If you are deleting more than one consecutive program line, start with the last line in the group.) 3. Key in the new instruction, if any. This replaces the one you - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 177
or number you want to change, then enter the desired corrections. 4. Press ‘ to end the equation. Program Memory Viewing Program Memory Pressing { e toggles the calculator into and out of program entry (PRGM annunciator on, program lines displayed). When Program-entry mode is active, the contents of - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 178
catalog to: „ Review the labels in program memory and the memory cost of each labeled program or routine. „ Execute a labeled program. (Press X or g while the label is displayed.) „ Display a labeled program. (Press { e while the label is displayed.) „ Delete specific programs. (Press { c while - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 179
calculator are the same, then you have correctly entered all the lines of the program. To see your checksum: 1. Press { Y { } for the catalog of program labels. 2. Display program (the "cylinder" program): Keys: (In RPN mode) Display: Description: { Y hold) / Displays label - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 180
instruction in a program to change the base mode will determine how input is interpreted and how output looks during and after program execution, but it does not affect the program lines as you enter them. Equation evaluation, SOLVE, and ³ FN automatically set Decimal mode. 12-22 Simple Programming - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 181
program lines below in the left and right columns. All non-decimal numbers are right-justified in the calculator's display. Notice how the number 13 appears as "D" in Hexadecimal mode. Decimal mode set: : : PRGM % PRGM : : Hexadecimal mode set: PRGM : : HEX % PRGM HEX - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 182
Now evaluate this polynomial for x = 7. Keys: (In ALG mode) Display: X A 7g %@ value 8 ) Description: 5 5x. 5x4 5x4 + 5x4 + 2 5x4 + 2x 5x4 + 2x3 Displays label A, which takes 93 bytes. Checksum and length. Cancels program entry. Description: Prompts for x. Result. 12-24 Simple - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 183
A more general form of this program for any equation Ax4 + Bx3 + Cx2 + Dx + E would be: h h h h Checksum and length: E41A 54 Simple Programming 12-25 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 184
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 185
mean and standard deviation. Routine D sets a limit of integration, executes routine Q, and displays the result. Routine Q integrates the function defined in routine F and finishes the probability calculation of Q(x). A routine typically starts with a label (LBL) and ends with an instruction that - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 186
Q in the "Normal and Inverse-Normal Distributions" program in chapter 16 is a subroutine (to calculate Q(x)) that is called from routine D by line Routine Q ends with a RTN instruction that sends program execution back to routine D (to store and display the result) at line D0004. See the flow - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 187
levels deep causes an error. Example: A Nested Subroutine. The following subroutine, labeled S, calculates the value of the expression a2 + b2 + c2 + d2 as part of a larger calculation in a larger program. The subroutine calls upon another subroutine (a nested subroutine), labeled Q, to do the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 188
In RPN mode, N€ P€ R€ "! "! "! "! €M €O €Q º ! Starts program other than the next line. This is called branching. Unconditional branching uses the GTO (go to) instruction to branch to a program - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 189
returns to its point of origination, so GTO is not used for subroutines. For example, consider the "Curve Fitting" program in chapter 16. The ! ' instruction branches execution from any one of three independent initializing routines to LBL Z, the routine that is the common entry point into - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 190
10000). For example, { V A0005. „ To a label: { V label -but only if program entry is not active (no program lines displayed; PRGM off). For example, { V A. Conditional Instructions Another way to alter the sequence of program execution is by a conditional test, a true/false test that compares - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 191
x≤0? {0? {≥} for x≥0? {/} for x=0? If you execute a conditional test from the keyboard, the calculator will display & or . For example, if x =2 and y =7, test x - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 192
flag is set, and skips one line if the flag is clear. Meanings of Flags The HP 33s has 12 flags, numbered 0 through 11. All flags can be set, cleared, and tested from the keyboard or by a program instruction. The default state of all 12 flags is clear. The three-key memory clearing operation - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 193
that caused the overflow. By testing flag 6 in a program, you can alter the program's flow or change a result anytime an overflow occurs. „ Flags 7, 8 and 9 control the display of fractions. Flag 7 can also be controlled from the keyboard. When Fraction-display mode is toggled on or off by pressing - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 194
moves to the next program line. 3. The equation is displayed without affecting the stack. You can clear the display by pressing b or ‡. Pressing any other key executes that key's function. 4. If the next program line is a PSE instruction, execution continues after a 1-second pause. The status of - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 195
line is skipped. This is the "Do if True" rule, illustrated under "Conditional Instructions" earlier in this chapter. If you test a flag from the keyboard, the calculator will display "& " or " ". It is good practice in a program to make sure that any conditions you will be testing start out in - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 196
Example: Using Flags. The "Curve Fitting" program in chapter 16 uses flags 0 and 1 to determine whether to take the natural logarithm of the X- and Y-inputs: „ Lines E0003 clear flags 0 and 1 to ensure that they will be set only as required for the four curve models. 13-12 Programming Techniques - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 197
Program Lines: (In RPN mode) $ @ $ . . . $ @ Description: Clears flag 0, the indicator for In X. Clears flag 1, the indicator for In Y. Sets flag 0, the indicator for In X. Clears flag 1, the indicator for In Y. - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 198
also contains examples of how the three fraction-display flags (7, 8, and 9) and the "message-display" flag (10) are used. Messages in this program are listed as MESSAGE and are entered as equations: 1. Set Equation-entry mode by pressing | H (the EQN annunciator turns on). 2. Press L letter for - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 199
Lines: (In ALG mode) Description: ! +F 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 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 200
Use the above program to see the different forms of fraction display: Keys: (In ALG mode) Display: Description: X F 2.53 g 16 g g #@ value @ value d g c g c g ‡ ) | y {} 0 Executes label F; prompts for a fractional number (V). Stores 2.53 in V; prompts for - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 201
A is less than or equal to B. Program lines: (In RPN mode) Checksum and length: D548 9 Description: It is easier to recall A than to remember where it is in the stack. . Calculates A - B. ! Replaces old A with new result. Recalls constant - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 202
time a loop function is executed in a program, it automatically decrements or increments a counter final-value . . . ! increment %! variable A DSE instruction is like a FOR-NEXT loop with a negative increment. or unspecified). This value does not change. An unspecified value for ii is assumed - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 203
, the loop-control number 0.050 for ISG means: start counting at zero, count up to 50, and increase the number by 1 each loop. The following program uses ISG to loop 10 times. The loop counter (0000001.01000) is stored in the variable Z. Leading and trailing zeros can be left off. Press - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 204
, recall, and manipulate the contents of i just as you can the contents of other variables. You can even solve for i and integrate using i . The functions listed below can use variable "i". STO i RCL i STO i RCL i INPUT i VIEW i ³ FN d i SOLVE i DSE i ISG i x < > i 13-20 Programming Techniques - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 205
(i) will address: ± 1 . . . ±26 ±27 ±28 ±29 ±30 ±31 ±32 ±33 ≥34 or ≤-34 or 0 variable A or label A . . . variable Z or label Z addressing. The INPUT(i) and VIEW(i) operations label the display with the name of the indirectly-addressed variable or register register. Programming Techniques 13-21 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 206
STO i) RCL i) XEQ(i) GTO(i) X(i) INPUT(i) VIEW(i) DSE(i) ISG(i) SOLVE(i) ³ FN d(i) FN=(i) Program Control with (i) Since the contents of i can change each time a program runs - or even in different parts of the same program - a program instruction such as ! 1L2 can branch to a different label - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 207
An index value in i is used by the program "Solutions of Simultaneous Equations - Matrix Inversion Method" in chapter 15. This program uses the looping instructions L and L in conjunction with the indirect instructions 1L2 and ! 1L2 to fill and manipulate a matrix. The first part of this - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 208
J is a loop that completes the inversion of the 3 × 3 matrix. Program Lines: (In RPN mode) Description: ! ª1L2 for next value. Returns to the calling program or to ! . Equations with (i) You can use (i) in an equation to specify a variable indirectly. Notice that - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 209
Lines: (In RPN mode) Description: Begins the program. Sets equations for execution. Disables equation prompting. ) Sets counter for 1 to 26. ! L Stores counter. Initializes sum. Checksum and length: AEC5 42 Starts - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 210
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 211
especially useful if the equation you're solving changes for certain conditions or if it requires repeated calculations. To solve a programmed function: 1. Enter a program that defines the function. (See "To write a program for SOLVE" below.) 2. Select the program to solve: press | W label. (You can - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 212
message for display (an equation with Flag 10 set), then the instruction is normally executed only once - it is not executed each time the program is called by SOLVE. However, if VIEW or a message is followed by PSE, then the value or message will be displayed for one second each time the program is - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 213
To begin, put the calculator in Program mode; if necessary, position the program pointer to the top of program memory. Keys: (In ALG mode) Display: Description: {e{ V ! Sets Program mode. Type in the program: Program Lines: (In ALG mode) Description: Identifies the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 214
prompts for N. Stores .005 in N; prompts for R. Stores .0821 in R; prompts for T. Calculates T. Stores 297.1 in T; solves for P. Pressure is 0.0610 atm. Example: Program Using Equation. Write a program that uses an equation to solve the "Ideal Gas Law." Keys: (In RPN mode) Display: Description - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 215
! ‡ ) Checksum and length of program: 36FF 21 Ends the program. Cancels Program-entry mode. Now calculate the change in pressure of the carbon dioxide if its temperature drops by 10 °C from the previous example. Keys: (In RPN mode) Display: Description: I L |W H P g g g ‘ 10 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 216
for solving an equation for an unknown variable appear in programs as: / label #variable The programmed SOLVE instruction does not produce a labeled display (variable = value) since this might not be the significant output for your program (that is, you might want to do further calculations - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 217
in i. / Defines program to solve. #1L2 Solves for appropriate variable. #$1L2 Displays solution. ! Ends program. Checksum and length: D82E 18 Calculates f (x,y). Include INPUT or equation prompting as required. Integrating a Program In chapter 8 you - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 218
though it can be any type of equation. If you want the equation to prompt for variable values instead of including INPUT instructions, make sure flag 11 is set. 4. End the program with a RTN. Program execution should end with the value of the function in the X-register. 14-8 Solving and Integrating - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 219
from 0 to 2; displays result. Restores Degrees mode. Using Integration in a Program Integration can be executed from a program. Remember to include or display format at the time the program runs. The two integration instructions appear in the program as: / label Solving and Integrating Programs - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 220
further calculations with this number before displaying it). If you do want this result displayed, add a PSE ( |f ) or STOP (g) instruction to display the result in the X-register after the ³ FN instruction. If the program contains a VIEW or STOP instruction, or a message for display (an equation - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 221
error). The SOLVE variable and ³ FN d variable instructions in a program use one of the seven pending subroutine returns in the calculator. (Refer to "Nested Subroutines" in chapter 13.) The SOLVE and ³ FN operations automatically set Decimal display format. Solving and Integrating Programs 14-11 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 222
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 223
input and output in rectangular or polar form. Angles between vectors can also be found. Z P R Y T X This program uses the following equations. Coordinate conversion: X = R sin(P) cos(T) R = X2 +Y2 + Z2 Y = R sin(P) sin(T) T = arctan (Y/X) Z = R cos(P) P = arctan Z X2 +Y2 Mathematics - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 224
= (U - X)i + (V - Y)j + (W - Z)k v1 × v2 = (YW - ZV )i + (ZU - XW)j + (XV - YU)k Dot Product: Angle between vectors (γ): D = XU + YV + ZW D G = arccos R1 × R2 where v1 = X i + Y j + Z k and v2=U i + V j + W k The vector displayed by the input routines (LBL P and LBL R) is V1. 15-2 Mathematics - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 225
! Saves P Checksum and length: E230 36 65¸ 8T´¸8º Defines the beginning of the polar input/display routine. Displays or accepts input of R. Displays or accepts input of T. Displays or accepts input of P. Calculates R cos(P) and R sin(P). Mathematics Programs 15-3 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 226
. % %65 " % ! % % & % º65 # % ! & % ' % º65 $ % ! ' % ! Loops back for polar conversion and display/input. Checksum and length: CE3C 33 Defines beginning of vector-addition routine. 15-4 Mathematics Programs - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 227
Program Lines: (In ALG mode) Description % ! % Saves X + U in X. # - & ! & Saves V + Y in Y. ' ! ' Saves Z + W in Z. ! Loops back for polar conversion and display/input. Checksum and length: 6ED7 33 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 228
Program Lines: (In ALG mode) Description ! Calculates (ZU - WX), which is the Y component. ! % º # . & Stores Y component. ! Loops back for polar conversion and display/input. Checksum and length: 6F95 81 65 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 229
Program Lines: (In ALG mode) Description $ ¸8º´θ8T Calculates the magnitude of Calculates angle. ! Displays angle. ! Loops back for polar display/ available for cross product. Program Instructions: 1. Key in the program routines; press ‡ when done - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 230
To key in a second vector, press X E review v1 in rectangular form, press X R, then press g repeatedly to see the individual elements. 9. If you added, subtracted, or computed the cross product, v1 has been replaced by the result, v2 is not altered. To continue calculations conversion capability to - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 231
&@ value '@ value @ ) !@ E (x) Description: Sets Degrees mode. Starts rectangular input/display routine. Sets X equal to 7.3. Sets Y equal to 15.7. Sets Z equal to -0.76 and calculates R, the radius. Calculates T, the angle in the x/y plane. Calculates P, the angle from the z-axis - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 232
1.07m 63 o 125 o F2 = 23 T = 80 o P = 74 o Y First, add the force vectors. Keys: (In ALG mode) Display: X P 17 g 215 g 17 g X E 23 g 80 g 74 g X A g @ value !@ value @ value @ 74. Adds the vectors and displays the resultant R. Displays T of resultant vector. 15-10 Mathematics Programs - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 233
product. Displays rectangular form of cross product. The dot product can be used to resolve the force (still in v2) along the axis of the lever. Keys: (In ALG mode) Display: Description: X P 1g Starts polar input routine. Defines the radius as one unit vector. Mathematics Programs 15 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 234
equal to 63. Calculates dot product. Calculates angle between resultant force vector and lever. Gets back to input routine. Solutions of Simultaneous Equations This program solves simultaneous linear equations in two or three unknowns. It does this through matrix inversion and matrix multiplication - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 235
! Returns to LBL A to review values. Checksum and length: 51AB 15 This routine inverts a 3 × 3 matrix. Calculates determinant and saves value for the division loop, J. Calculates E' × determinant = AI - CG. Calculates F' × determinant = CD - AF. Mathematics Programs 15-13 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 236
Program Lines: (In RPN mode) ! L Description Calculates H' × determinant = BG - AH. Calculates I' × determinant = AE - BD. Calculates A' x determinant = EI - FH, Calculates B' × determinant = CH - BI. Calculates C' × determinant = BF - CE. Stores B'. Calculates D' × determinant = FG - - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 237
Returns to the calling program or to ! . Checksum and length: 1FCF 15 This routine multiplies a column matrix and a 3 × 3 matrix. Sets index value to point, to last element in first row. Sets index value to point to last element in second Mathematics Programs 15-15 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 238
Program Lines: (In RPN mode) Description row. % Sets index value to point to last element in third row. Checksum and length: DA21 54 This routine calculates product of column vector and row pointed to by index value. ! L Saves index value in i. - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 239
Program Lines: (In RPN mode) Description Calculates A × E × I. º - Calculates (A × E × I) + (D × H × C). - Calculates (A × E × I) + (D × H × C) + (G × F × B). . (A × E × I) + (D × H × C) + (G - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 240
L. Use 1 for coefficient I. Not all systems of equations have solutions. Example: For the system below, compute the inverse and the system solution. Review the inverted matrix. Invert the matrix again and review the result to make sure that the original matrix is returned. 23X + 15Y + 17Z = 31 8X - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 241
and displays the determinant. Multiplies by column vector to compute X. Calculates and displays Y. Calculates and displays Z. Begins review of the inverted matrix. Displays next value. Displays next value. Displays next value. Displays next value. Displays next value. Mathematics Programs 15 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 242
next value. Inverts inverse to produce original matrix. Begins review of inverted matrix. Displays next value, ...... and so on. Polynomial Root Finder This program finds the roots of a polynomial of order 2 through 5 with real coefficients. It calculates both real and complex roots. For this - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 243
L = J2 − a2 + y0 × (the sign of JK - a1/2) M = K 2 − a0 Roots of the fourth degree polynomial are found by solving these two quadratic polynomials. A quadratic equation x2 + a1x + a0 = 0 is solved by the formula x1,2 = − a1 2 ± ( a1 )2 2 − a0 If the discriminant d = (a1/2)2 - ao ≥ 0, the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 244
Program Listing: Program Lines: (In RPN mode) Description Defines the beginning of the polynomial root finder routine. Prompts for and done. ! Checksum and length: 2582 21 Starts solver setup routine. Stores location of coefficients to use. 15-22 Mathematics Programs - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 245
Program Lines: (In RPN mode) Description ! % First initial guess. -+. Second initial guess. / Specifies routine to solve. # % Solves root. Complex roots? Returns if complex roots. Calculates - a1/2 - d Calculates - a1/2 + d Mathematics Programs 15-23 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 246
Program Lines: (In RPN mode) ! Checksum and length: B9A7 81 Description Starts second-order solution routine. Gets L. Gets M. ! ! Calculates and displays two roots. Checksum and length: DE6F 12 Starts third-order - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 247
Program Lines: (In RPN mode) Checksum and length: C7A6 51 Description % Starts fourth-order pointer to the cubic coefficients. Solves for real root and puts a0 and a1 for second-order polynomial on stack. Discards polynomial function value. Solves for remaining roots of cubic - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 248
Program Lines: (In RPN mode) Description @ Complex roots? ! Calculate four roots of remaining fourth-order polynomial. If not complex roots, determine largest real root (y0) º6¸@ º65¸ º6¸@ º65¸ ! - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 249
Uses quadratic routine to calculate two roots. Checksum and length: 410A 6 @ Starts routine to display two real roots or two complex roots. Gets the first real root. Stores the first real root. Displays real root or real part of complex root. Gets the second real root - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 250
Program Lines: (In RPN mode) Description ! " Displays complex roots if any. ! % Stores second real root. Displays second real root. ! Returns to calling routine. Checksum and length: 96DA 30 " " Starts routine to display complex roots. " ! L - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 251
computations, the program may produce values that are not true roots of the polynomial. The only way to confirm the roots is to evaluate the polynomial manually to see if it is zero at the roots. For a third- or higher-order polynomial, if SOLVE cannot find a real root, the error is displayed. You - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 252
roots of x5 - x4 - 101x3 +101x2 + 100x - 100 = 0. Keys: (In RPN mode) Display: Description: X P 5g 1^g 101 ^ g 101 g 100 g 100 ^ g g g A; calculates the first root. Calculates the second root. Displays the third root. Displays the fourth root. Displays the fifth root. 15-30 Mathematics Programs - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 253
Keys: (In RPN mode) Display: Description: X P 4g 8^‘4 qg 13 ^ ‘ 4 qg 10 ^ ‘ 4 qg 22 ‘ 4 q g 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 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 254
= 0 Keys: (In RPN mode) Display: Description: X P 2g 1g 6 ^g g @ value @ value @ value Starts the polynomial root finder; prompts for order. Stores 2 in F; prompts for B. Stores 1 in B; prompts for A. Stores -6 in A; calculates the first root. Calculates the second root. Coordinate - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 255
y y' Old coordinate x P system [0, 0] u yv x' x [m, n] θ New coordinate system Mathematics Programs 15-33 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 256
# Stores y-coordinate in variable V. º65¸ Swaps positions of coordinates back. #$ " Halts program to display U. Halts program to display V. ! Goes back for another calculation. Checksum and length: 921A 69 This routine converts from the new system to the old - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 257
of the coordinates back. Halts the program to display X. #$ & Halts the program to display Y. ! Goes back for another calculation. Checksum and length: 8C82 66 Flags Used: None. Program Instructions: 1. Key in the program routines; press ‡ when done. 2. Press X D to - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 258
P3,which are currently in the (X, Y) system, to points in the (X', Y') system. Convert point P'4, which is in the (X',Y') system, to the (X,Y) system. 15-36 Mathematics Programs - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 259
&@ value ) Description: Sets Degrees mode since T is given in degrees. Starts the routine that defines the transformation. Stores 7 in M. Stores -4 in U. Stores 27 in T. Starts the old-to-new routine. Stores -9 in X. Stores 7 in Y and calculates U. Calculates V. Mathematics Programs 15-37 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 260
for next problem. Stores -5 in X. Stores -4 in Y. Calculates V. Resumes the old-to-new routine for next problem. Stores 6 in X . Stores 8 in Y and calculates U. Calculates V. Starts the new-to-old routine. Stores 2.7 in U. Stores -3.6 in V and calculates X. Calculates Y. 15-38 Mathematics Programs - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 261
coefficients, m and b. The program includes a routine to calculate the estimates xˆ and yˆ . (For definitions of these values, see "Linear Regression" in chapter 11.) Samples of the curves and the relevant equations are shown below. The internal regression functions of the HP 33s are used to compute - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 262
12 error will occur if a negative number is entered for these cases. Data values of large magnitude but relatively small differences can incur problems of precision, as can data values of greatly different magnitudes. Refer to "Limitations in Precision of Data" in chapter 11. 16-2 Statistics - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 263
Program Listing: Program Lines: (In RPN mode) Description This routine sets, the status for the straight-line model. Enters index value for later storage in models. Clears the statistics registers. Stores the index value in i for indirect addressing. Statistics Programs 16-3 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 264
Program Lines: (In RPN mode) Description ' Sets the loop counter to zero for the first E H% Defines the start of the output routine Calculates the correlation coefficient. Stores it in R. Displays the correlation coefficient. Calculates the coefficient b. If flag 1 is set takes - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 265
Program Lines: (In RPN mode) Description ! Stores b in B. Displays value. P Calculates coefficient m. ! Stores m in M. Displays value. Checksum and length: 9CC9 36 Defines the beginning of the estimation (projection) loop. 1L2 & ! & Displays, - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 266
Program Lines: (In RPN mode) Description % Calculates yˆ = M In X + B. ! Returns to the calling routine. Checksum and length: A5BB 18 This subroutine calculates xˆ for the logarithmic model. ! . L Restores index value to its original value. - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 267
Program Lines: (In RPN mode) Description ! ! !¸% Calculates Y= B(XM). ! ! Returns to the calling routine. Checksum and length: 018C 18 This subroutine calculates Program instructions: 1. Key in the program routines; press ‡ when done. 2. Press X and select the type - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 268
(with the &@value prompt still visible), press g again (displaying the %@value prompt) and press X U to undo (remove) the last data pair. If you discover that you made to indirectly address the correct xˆ -, yˆ -projection equation. Statistical accumulation and computation. 16-8 Statistics Programs - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 269
value of 101. X 40.5 38.6 37.9 36.2 35.1 34.6 Y 104.5 102 100 97.5 95.5 94 Keys: (In RPN mode) Display: Description: X S 40.5 g 104.5 g 38.6 you can see how to correct incorrect entries. Keys: (In RPN mode) Display: Description: 379 g g X U 37.9 g Enters wrong x-value - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 270
35 Calculates the correlation coefficient. Calculates regression coefficient B. Calculates regression coefficient M. Prompts for hypothetical x-value. Stores 37 in X and calculates yˆ . Stores 101 in Y and calculates type of curve. You will need to reenter the data values each time you run the program - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 271
the inverse: given a value Q(x), the program calculates the corresponding value x. y "Upper tail" area Q [x] x x ³ Q(x) = 0.5 − 1 e dx x −((x −x )÷σ )2 ÷2 σ 2π x This program uses the built-in integration feature of the HP 33s to integrate the equation of the normal frequency curve. The - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 272
Stores default value for standard deviation. ! "! Prompts for and stores standard deviation, S. ! Stops displaying value of standard deviation. Checksum and length: D72F 48 This routine calculates Q(X) given X Prompts for and stores X Calculates upper tail area Stores - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 273
Program Lines: (In RPN mode) Description Adds the correction to yield a new Xguess. ! ! ) ! º6¸@ Tests % Displays the calculated value of X. ! ! Loops to calculate another X. Checksum and length: 0E12 63 This subroutine calculates the upper-tail - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 274
deviations. Computation time is significantly less with a lower number of displayed digits. In routine Q, the constant 0.5 may be replaced by 2 and . You do not need to key in the inverse routine (in routines I and T) if you are not interested in the inverse capability. Program Instructions - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 275
The result, Q(X), is displayed. 8. To calculate Q(X) for a new X with the same mean and standard deviation, press g and go to step 7. 9. To calculate X given Q(X), press problem is stated in terms of standard deviations, use the default value of zero for M and 1 for S. Keys: (In RPN mode) Display - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 276
by pressing g. Keys: (In RPN mode) Display: Description: g 2g 10000 z ) Resumes program. Enters X-value of 2 and calculates Q(X). Multiplies by the population for the revised estimate. Example 2: The mean of a set of test scores is 55. The standard deviation is 15.3. Assuming that the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 277
: (In RPN mode) Display: Description: X I 0.1 g g 0.8 g ) Starts the inverse routine. Stores 0.1 (10 percent) in Q(X) and calculates X. Resumes the inverse routine. Stores 0.8 (100 percent minus 20 percent) in Q(X) and calculates X. Grouped Standard Deviation The standard deviation of - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 278
Program Listing: Program Lines: (In ALG mode) Description Start grouped standard deviation program. ; Clears statistics registers (28 through 33). ! Clears the count N. Checksum and length: EF85 24 Input statistical data points. - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 279
. Checksum and length: 3080 117 Calculates statistics for grouped data. Uº Grouped standard deviation. ! Displays grouped standard deviation. º Weighted mean. ! #$ Displays weighted mean. ! Goes back for more - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 280
data pair has been input, press X G to calculate and display the grouped standard deviation. 8. Press g to display the weighted mean of the grouped data. 9. To add additional data points, press g and continue at step 3. To start a new problem, start at step 2. Variables Used: X F N S M i Register - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 281
22 37 17 26 37 43 73 115 Keys: (In ALG mode) Display: Description: X S 5g 17 g g 8g 26 g g 14 g 37 g %@ value @ value 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 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 282
fifth xi. 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. 16-22 Statistics Programs - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 283
Programs and Equations Time Value of Money Given any four of the five values in the "Time-Value-of-Money equation" (TVM), you can solve for the fifth value. This equation is useful in a wide variety of financial applications such as consumer and home loans and savings accounts. The TVM equation - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 284
Selects Equation mode. Starts entering equation. Terminates the equation. Checksum and length. Remarks: The TVM equation requires that I must be non-zero to avoid a # & error. If you're solving for I and aren't sure of its current value, press 1 I I before you begin the SOLVE calculation - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 285
SOLVE instructions: 1. If your first TVM calculation is to solve for interest rate, I, press 1 I I. 2. Press | H. If necessary, press ™ or š to scroll through the equation list until you come to the TVM equation. 3. Do one of the following five operations: a. Press N to calculate the number of - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 286
N = 36 months F = 0 P = ? Keys: (In RPN mode) Display: Description: {%} 2 | H (š as needed ) P 10.5 ‘ 12 q g 36 g 0g 7250 ‘ 1500 … g Selects FIX 2 display format. º º1.1-ªDisplays the leftmost part of the TVM equation. @ Selects P; prompts for I. value @ Converts your - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 287
the interest rate, I, from part 2 is not zero, so you won't get a error when you calculate the new I. Keys: (In RPN mode) Display: Description: |H F º º1.1-ªDisplays leftmost part of the TVM equation. @ Selects F; prompts for P. . ) Miscellaneous Programs and Equations 17-5 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 288
prompts for N. Stores 24 in N; prompts for B. Retains 5750 in B; calculates F, the future balance. Again, the sign is negative, indicating that you must, pay out this money. Sets FIX 4 display format. Prime Number Generator This program accepts any positive integer greater than 3. If the number is - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 289
LBL Y Note: x is the value in the X- r e g i s t e r. VIEW Prime LBL Z P+2 →x Start LBL P x→ P 3→ D LBL X yes x = 0? no yes no Miscellaneous Programs and Equations 17-7 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 290
Program Listing: Program Lines: (In ALG mode) Description This routine displays prime number P Checksum and length: AA7A 6 This routine adds 2 to P Checksum and length: 8696 21 This routine the number is not prime, tries next possibility. 17-8 Miscellaneous Programs and Equations - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 291
display routine. % Calculates the next possible factor, D + 2. % ! - Branches to test potential prime with new factor. Checksum and length: 161E 57 Flags Used: None. Program Instructions: 1. Key in the program is the next prime number? Miscellaneous Programs and Equations 17-9 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 292
Keys: (In ALG mode) 789 X P g Display: / Description: Calculates next prime number after 789. Calculates next prime number after 797. 17-10 Miscellaneous Programs and Equations - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 293
Part 3 Appendixes and Reference - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 294
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 295
program entry only), the statistics registers, or all of user memory (not during program entry). Q: What does an "E" in a number (for example, ).) mean? A: Exponent of ten; that is, 2.51 × 10-13. Q: The calculator has displayed the message What should I do? Support, Batteries, and Service - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 296
(32 to 113 °F). „ Storage temperature: -20 to 65 °C (-4 to 149 °F). „ Operating and storage humidity: 90% relative humidity at 40 °C (104 °F) maximum. Changing the Batteries The calculator is powered by two 3-volt lithium coin batteries, CR2032. Replace the batteries as soon as possible when the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 297
will be erased. 3. Turn the calculator over and slide off the battery cover. 4. Never remove two old batteries at the same time, to prevent memory lose. Remove one of the two batteries. Press down the holder. Push the plate in the shown direction and lift it. Support, Batteries, and Service A-3 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 298
when you release all three keys. 3. Remove the batteries (see "Changing the Batteries") and lightly press a coin against both battery contacts in the calculator. Replace the batteries and turn on the calculator. It should display 4. If the calculator still does not respond to keystrokes, use - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 299
it requires service. 2. If the calculator passes the self-test, you may have made a mistake operating the calculator. Reread portions of the manual and check "Answers to Common Questions" (page A-1). 3. Contact the Calculator Support Department listed on page A-7. The Self-Test If the display can - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 300
Warranty HP 33s Scientific Calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above. If HP receives notice of such - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 301
REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU. Service Europe Country : 35-89640009 +33-1-49939006 +49-69-95307103 +420-5-41422523 +31-2-06545301 +39-02-75419782 Support, Batteries, and Service - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 302
European countries +47-63849309 +351-229570200 +34-915-642095 +46-851992065 +41-1-4395358 (German) +41-22-8278780 (French) +39-02-75419782 (Italian) +420-5-41422523 +44-207-4580161 +420-5-41422523 +27-11 1-800-711-2884 1-800-999-5105 1-877-232-0589 0-800-011-0524 A-8 Support, Batteries, and Service - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 303
://www.hp.com for the latest service and support information. Regulatory Information This section contains information that shows how the HP 33s scientific calculator complies with regulations in certain regions. Any modifications to the calculator not expressly approved by Hewlett-Packard could - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 304
under normal operation (per ISO 7779): LpA - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 305
„ Which operations affect stack lift. Managing Calculator Memory The HP 33s has 31KB of user memory available to you for any combination of stored data (variables, equations, or program lines). SOLVE, ³ FN, and statistical calculations also require user memory. (The ³ FN operation is particularly - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 306
F. To see the memory requirements of an equation in a program: 1. Display the program line containing the equation. 2. Press | to see the checksum and length. For example, / /. To manually deallocate the memory allocated for a SOLVE or ³ FN calculation that has been interrupted, press - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 307
is successful. Category CLEAR ALL Angular mode Base mode Contrast setting Decimal point Denominator (/c value) Display format Flags Fraction-display mode Random-number seed Equation pointer Equation list FN = label Program pointer Program memory Stack lift Stack registers Variables Unchanged - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 308
Memory may inadvertently be cleared if the calculator is dropped or if power is interrupted. The Status they also disable stack lift. The INPUT function disables stack lift as it halts a program for prompting (so any number you then enter writes over the X-register), but it enables stack lift when - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 309
Y { }** V EQN FDISP Errors V label nnnn e and program entry Switching Digit entry binary windows ¼ Except when used like CLx. ¼¼ Including all operations performed while the catalog is displayed except {# } ‘ and { } X, which enable stack lift. User Memory and the Stack B-5 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 310
stores a different value in the LAST X register than the sequence x h variable Ù does. The former stores x in LAST X; the latter stores the recalled number in LAST X. B-6 User Memory and the Stack - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 311
mode, including, „ Two-number arithmetic „ Chain calculation „ Reviewing the stack „ Coordinate conversions „ Operations with complex numbers „ Integrating an equation , RND, RAND, IP, FP, INTG, SGN, ABS, ex,10x, unit conversion. 3. x y and yx. 4. nPr, nCr, %CHG. 5. ×, ÷, INT÷, Rmdr. 6. - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 312
the first number, press the operator (›, …, z, q), enter the second number, and finally press the ‘ key. To Calculate: 12워3 12 - 3 12 × 3 12 ÷ 3 Press: 12 ›3 ‘ 12 … 3 ‘ 12 z 3 ‘ 12 q 3 ‘ Display: Power Functions In ALG mode, to calculate a number y raised to a power x, key in y x, then - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 313
12% greater than 25 Press: 200 z 27 Q ‘ 200 … 27 Q ‘ 25 › 12 Q ‘ Display: º 0 0 0/ ) To Calculate: x% of y Percentage change from y to x. (y≠ 0) Press: yzxQ‘ y|Tx‘ Compare these keystrokes in RPN and ALG modes: 27% of 200 RPN Mode 200 ‘ 27 Q 200 less 27% 200 ‘ 27 Q… ALG - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 314
$16.12 last year. What is the percentage change from last year's price to this year's? Keys: Display: Description: 16.12 | T 15.76 ‘ person safety committee. How many different combinations of people are possible? Keys: Display: Description: 24 { \ 6 ‘ QT / Total number of combinations - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 315
30 ¯ º y 85 Ã 12 º | ¸ 9 Ï Display: Description: No calculation is done. Calculates 85 − 12. Calculates 30/73. Calculates 30/(85 − 12) × 9. You can omit the multiplication sign (×) before a left parenthesis. Implied multiplication is not available in Equation mode. For example, the expression - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 316
360 ‘ or 750 z 12 q 360 ‘ In the second case, the q key acts like the ‘ key by displaying the result of 750 × 12. Here's a longer chain calculation: 456 − 75 × 68 18.5 1.9 This calculation can be written as: 456 … 75 ‘ q 18.5 z 68 q 1.9 ‘. Watch what happens in the display as you key it in: Keys - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 317
‘, the result is not placed into X1, X2 etc.) Only after evaluating equations, programs, or integrating equations, the values of the four registers will be the same as in RPN mode. Coordinate Conversions To convert between rectangular and polar coordinates: 1. Enter the coordinates (in rectangular - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 318
. Use parentheses to impose the required order of operations. Calculates x. Displays y. Integrating an Equation 1. Key in an equation. (see "Entering Equations into the Equation List" in chapter 6) and leave Equation mode. 2. Enter the limits of integration: key in the lower limit and press [, then - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 319
, x, then the function key. 2. Type the imaginary part, y, then press {G. Fox example, to do 2 + i 4, press 2 › 4 {G. To view the result of complex operations웛 After keying in the complex number, press ‘ to calculate. Then the real portion of the result is displayed; press š to view the imaginary - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 320
Result is 9.1545 - i 4.1689 Examples: Evaluate the expression z 1 ÷ (z2 + z3), where z1 = 23 + i 13, z2 = -2 + i z3 = 4 - i 3 Keys: Display: | ] 23 ›13 {G|` q|]2^› 1{G›4 … 3 { G |`‘ š 1워L2ª1 1워L2ª1 Description: Real part of result. Result is 2.5000 + i 9.0000 C-10 ALG - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 321
the rightmost digits are replaced with an ellipsis to indicate it is too long to be displayed. Here are some examples of arithmetic in Hexadecimal, Octal, and Binary modes: Example: Keys: 12F Ù E9A Ï 7760 Ã 4326 Ï 12F16 + E9A16 = ? Display: Description: Sets base 16; HEX annunciator on - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 322
. 5A016 + 100110002 =? Set base 16; HEX annunciator on. Changes to base 2; BIN annunciator on. Result in binary base. Result in hexadecimal base. Restores decimal base. Entering Statistical Two-Variable Data In ALG mode, remember to enter an (x, y) pair in - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 323
Keys: { c {´} 4 [ 20 6 [ 400 { { 6 [ 40 4 [ 20 { 5 [ 20 Display: 8 Q/) 8 Q 8 Q/) 8 Q/) 8 Q/) 8 Q/) Description: Clears existing statistical data. Enters the first new data pair. Display shows n, the number of data pairs you - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 324
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 325
SOLVE operation beyond that given in chapter 7. How SOLVE Finds a Root SOLVE first attempts to solve the equation directly for the unknown variable. If the attempt fails, SOLVE changes the calculator, and the function must be mathematically defined where the iterative search occurs. SOLVE always - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 326
(x) x a f (x) x b f (x) x x c d Function Whose Roots Can Be Found In most situations, the calculated root is an accurate estimate of the theoretical, infinitely precise root of the equation. An "ideal" solution is one for which f(x) = 0. However, a very small non-zero value for f(x) is often - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 327
Interpreting Results The SOLVE operation will produce a solution under either of the following conditions: „ If it finds an estimate for which f(x) equals zero. (See figure a, below.) „ If it finds an estimate where f(x) is not equal to zero, but the calculated root is a 12-digit number adjacent - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 328
mode. Enters the equation. Checksum and length. Cancels Equation mode. Now, solve the equation to find the root: Keys: Display: Description: 0 I X 10 |H X .) . Initial guesses for the root. Selects Equation mode; displays the left end of the equation. Solves for X; displays - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 329
length. Cancels Equation mode. Now, solve the equation to find its positive and negative roots: Keys: Display: Description: 0 I X 10 |H X | 0 I X 10 ^ |H X | _ %:-%. Your initial guesses for the positive root. Selects Equation mode; displays the equation. Calculates the - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 330
and a Pole Example: Discontinuous Function. Find the root of the equation: IP(x) = 1.5 Enter the equation: Keys: Display: Description: |H |"LX| ` | ’ 1.5 ‘ | ‡ 1%2 Selects Equation mode. Enter the equation. Checksum and length. Cancels Equation mode. Now, solve to find the root - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 331
relatively large value for f(x). The problem is that there is no value of equation as an expression. Keys: Display: Description: |H L X q |]L X 2 … 6 |`…1 ‘ | ‡ 1%:. 2. / Selects Equation mode. Enters the equation. Checksum and length. Cancels Equation mode. More about Solving - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 332
Your initial guesses for the ) _ root. %ª1%:. 2. Selects Equation mode; displays the equation. ! No root found for f(x). 8 8 8 ) f(x) is relatively large. When SOLVE Cannot Find a Root Sometimes SOLVE fails to find a root. The following conditions cause the message - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 333
. Calculate the root of this parabolic equation: x2 - 6x + 13 = 0. It has a minimum at x = 3. Enter the equation as an expression: Keys: Display: Description: |H L X 2 …6zLX› 13 ‘ | / Selects Equation mode. Enters the equation. Checksum and length. More about Solving D-9 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 334
|H 10 … L X |`‘ | ‡ .005 I X 5 |H .#1%2 1%2 X %/ ) Description: Selects Equation mode. Enters the equation. Checksum and length. Cancels Equation mode. Your positive guesses for the root. Selects Equation mode; displays the equation. Solves for x using guesses 0.005 and - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 335
mode. First attempt to find a positive root: Keys: Display: Description: 0I X 10 |H X Your positive guesses for the _ root. !1%ª1%- )22 Selects Equation mode; displays the left end of the equation. %/ Calculates the root using ) guesses 0 and 10. More about Solving - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 336
Equation mode. Displays the final estimate of 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: 6¸@ 5¸@ D-12 More about Solving - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 337
of 10-8 and -10-8. Keys: (In RPN mode) Display: Description: a8^IX 1^a8^ |W J X %/ .) Enters guesses. Selects program "J" as the function. Solves for X; displays the result. Round-Off Error The limited (12-digit) precision of the calculator can cause errors due to rounding off - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 338
Underflow occurs when the magnitude of a number is smaller than the calculator can represent, so it substitutes zero. This can affect SOLVE results. For example, consider the equation 1 x2 whose root is infinite in value. Because of underflow, SOLVE returns a very large value as a root. (The - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 339
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 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 340
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 approximations calculated integration algorithm in the HP 33s is one of the rarely occur in problems related to actual - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 341
(x) x With this number of sample points, the algorithm will calculate the same approximation for the integral of any of the functions shown , which is virtually the largest number you can key into the calculator. Try it and see what happens. Enter the function f(x) = xe-x. More about Integration E-3 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 342
level and limits of integration. Selects Equation mode; displays the equation. Approximation of the integral. The answer returned by the calculator is clearly incorrect, since the actual integral ∞ ∞ of f(x) = xe-x from zero to is exactly 1. But the problem is not that was represented by 10499 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 343
when this particular function is integrated over this particular interval. (For better approaches to problems such as this, see the next topic, "Conditions That Prolong Calculation Time.") Fortunately, functions exhibiting such aberrations (a fluctuation that is uncharacteristic of the behavior of - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 344
two illustrations.) Considering the variations or fluctuation as a type of oscillation in the function, the criterion of interest calculation will finish, and the more reliable will be the resulting approximation. f (x) Calculated integral of this function will be accurate. a f (x) Calculated - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 345
so large as 10499 - say 103. Rerun the previous integration problem with this new limit of integration: Keys: 0‘a 3 |H | X Display 1.%2 Description: New upper limit. Selects Equation mode; displays the equation. Integral. (The calculation takes a minute or two.) More about Integration E-7 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 346
required over the smaller interval. Consequently, several more iterations are required over the larger interval to achieve an approximation with the same accuracy, and therefore calculating the integral requires considerably more time. E-8 More about Integration - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 347
such an integral, you can modify the problem so that the calculation time is considerably reduced. Two such techniques are subdividing the interval of integration and transformation of variables. These methods enable you to change the function or the limits of integration so that the integrand - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 348
- HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 349
to solve a program while an integration calculation was running. The catalog of variables ( { Y {# } ) indicates no values stored. The calculator is executing a function that might take a while. Allows you to verily clearing the equation you are editing. (Occurs only in Equation-entry mode.) Allows - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 350
The calculator is calculating the integral of an equation or program. This might take a while. A running SOLVE or ∫ FN operation was interrupted by pressing Å or ¥. Data error: Attempted to calculate combinations or permutations with r >n, with non-integer r or n, or with n ≥1016. - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 351
SOLVE cannot find the root of the equation using the current initial guesses (see page D-8). 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 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 352
# !12 !! The calculator is solving an equation or program for its root. This might take a while. Attempted to calculate the square root of a negative number. Statistics error: „ Attempted to do a statistics calculation with n = 0. „ Attempted to calculate sx sy, xˆ , yˆ , - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 353
end of the table. Name +/- + - × ÷ ^ b Keys and Description Page ¼ ^ Changes the sign of a number. 1-14 1 › Addition. Returns y + x. 1-17 1 … x; clears a menu; erases last function keyed in an equation; starts equation editing; deletes a program step. 1-4 1-9 6-3 12-6 Operation Index G-1 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 354
to previous equation in equation list; moves program pointer to previous step. 1-24 6-3 12-9 12-18 Displays next entry in catalog; moves to next equation in equation list; moves program pointer to next line (during program entry); executes the current program line (not during program entry). 1-24 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 355
r€y,x Keys and Description Accumulates (y, x) into statistics registers. { Removes (y, x) from statistics registers. | {;º} Returns the sum of x- | {σº} Returns population standard deviation of x-values: ¦(xi − x)2 ÷ n | {σ¸} Returns population standard deviation of y-values: ¦(yi − - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 356
¼ | { ³ G _} variable Integrates the displayed equation or the program selected by FN=, using lower limit of the variable of mode. 1-10 { Common exponential. 6-15 2 Returns 10 raised to the specified power (antilogarithm). {} Selects display of all significant digits. 1-20 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 357
of the regression line: y - m x . 11-10 1 Displays the base-conversion menu. 10-1 { x {} Selects Binary (base 2) mode. 10-1 Turns on calculator; clears x; clears messages and prompts; cancels menus; cancels catalogs; cancels equation entry; cancels program entry; halts execution of an - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 358
indicated variable or program from a MEM catalog; clears displayed equation. 1-6 1-24 Clears all stored data, equations, and programs. 1-24 Clears all programs (calculator in Program mode). 12-20 Clears the displayed equation (calculator in Program mode). 12-6 { c {´} Clears statistics - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 359
Name CMPLX × CMPLX ÷ CMPLX1/x CMPLXCOS CMPLXex CMPLXLN CMPLXSIN CMPLXTAN CMPLXyx Cn,r COS Keys and Description Page ¼ { G z Complex 9-2 multiplication. Returns (z1x + i z1y) × (z2x + i z2y). { G q Complex 9-2 division. Returns (z1x + i z1y) ÷ (z2x + i z2y). { G Complex 9-2 reciprocal - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 360
cosh x. 4-6 1 Functions to use 40 physics 4-8 constants. { x {} Selects Decimal mode. 10-1 Ÿ {} 4-4 Selects Degrees angular mode. { v Radians to degrees. 4-13 1 Returns (360/2π) x. Displays menu to set the display format. 1-19 | m variable Decrement, Skip if Equal or less - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 361
4-13 1 Turns on and off Fraction-display 5-1 mode. {%} n Selects Fixed display with n decimal places: 0 ≤ n ≤ 11. 1-19 Displays the menu to set, clear, and test flags. 13-11 | W label Selects labeled program as the current function (used by SOLVE and ³ FN). | ? Fractional part of x. 14 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 362
to line nnnn of program label. 12-19 {V Sets program pointer to PRGM TOP. 12-19 HEX { x {%} 10-1 Selects Hexadecimal (base 16) mode. { Displays the HYP_ prefix for 4-6 hyperbolic functions. €HMS | u 4-12 1 Hours to hours, minutes, seconds. Converts x from a decimal fraction - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 363
equal to or less than given number. { ‰ variable Recalls the variable to the X-register, displays the variable's name and value, and halts program execution. Pressing g (to resume program execution) or š (to execute the current program line) stores your input in the variable. (Used only in - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 364
slope of the regression line: [Σ(xi- x )(yj- y )]÷Σ(xi- x )2 Displays the amount of available memory and the catalog menu. 1-24 Begins catalog of programs. 12-20 Begins catalog of variables. 3-3 Displays menu to set angular modes and the radix () or 8 ). 1-18 4-4 { {Q} 11-10 1 Returns - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 365
mode. 10-1 Turns the calculator off. 1-1 { _ Permutations of n items 4-14 2 taken r at a time. Returns n!÷(n - r)!. Activates or cancels (toggles) Program-entry mode. 12-5 | f Pause. Halts program execution briefly to display x, variable, or equation, then resumes. (Used only in programs - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 366
end of a program; the program pointer returns to the top or to the calling routine. 12-3 13-2 Roll down. 2-3 Moves t to the Z-register, z to the C-6 Y-register, y to the X-register, and x to the T-register in RPN mode. Displays the X1~X4 menu to review the stack in ALG mode. G-14 Operation - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 367
the C-6 T-register, y to the Z-register, and x to the Y-register in RPN mode. Displays the X1~X4 menu to review the stack in ALG mode. Displays the standard-deviation Menu. 11-4 { } n Selects Scientific display with n decimal places. (n = 0 through 11.) 1-19 | i Restarts the random-number - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 368
equation program execution at the current program line; stops a running program and displays the X-register. 12-17 Displays the summation menu. 11-4 | {Uº} 11-6 1 Returns sample standard deviation of x-values: ¦(xi − x )2 ÷ (n − 1) | {U¸} 11-6 1 Returns sample standard deviation - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 369
. Returns tan x. { U Hyperbolic tangent. Returns tanh x. | Š variable Displays the labeled contents of variable without recalling the value to the stack. 4-3 1 4-6 1 3-3 12-13 Evaluates the displayed equation. 6-12 X label Executes the program identified by label. ! Square of x. { $ Cube of - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 370
13-7 { n {>} If x>y, executes next program line; if x≤y, skips next program line. 13-7 { n {≥} If x≥y, executes next program line; if x - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 371
line. 13-7 | o {>} If x>0, executes next program line; if x≤0, skips next program line. 13-7 | o {≥} If x≥0, executes next program line; if x - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 372
Name yx Keys and Description Power. Returns y raised to the xth power. Notes: 1. Function can be used in equations. 2. Function appears only in equations. Page ¼ 4-2 1 G-20 Operation Index - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 373
13-22 ALG, 1-10 compared to equations, 12-4 in programs, 12-4 Algebraic mode, 1-10 ALL format. See display format in equations, 6-5 in programs, 12-6 setting, 1-20 alpha characters, 1-3 angles between vectors, 15-1 converting format, 4-13 converting units, 4-13 implied units, 4-4, A-2 angular mode - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 374
12-18 balance (finance), 17-1 base affects display, 10-4 arithmetic, 10-2 converting, 10-1 default, B-3 programs, 12-22 setting, 10-1, 14-11 base mode default, B-3 equations, 6-5, 6-10, 12-22 fractions, 5-2 programming, 12-22 setting, 12-22, 14-11 batteries, 1-1, A-2 Bessel function, 8-2 best-fit - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 375
18, A-1 degrees angle units, 4-4, A-2 converting to radians, 4-13 denominators controlling, 5-5, 13-9, 13-14 range of, 1-22, 5-1, 5-2 setting maximum, 5-4 digit-entry cursor backspacing, 1-5, 6-8, 12-6 in equations, 6-5 in programs, 12-6 meaning, 1-15 discontinuities of functions, D-5 display Index - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 376
1-20. See also display format EQN annunciator in equation list, 6-4, 6-6 in Program mode, 12-6 EQN LIST TOP, 6-7, F-1 Index-4 equality equations, 6-9, 6-10, 7-1 equation list adding to, 6-4 displaying, 6-6 editing, 6-8 EQN annunciator, 6-4 in Equation mode, 6-3 operation summary, 6-3 Equation mode - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 377
, 15-20 precedence of operators, 6-13 prompt for values, 6-10, 6-12 prompting in programs, 13-10, 14-1, 14-8 roots, 7-1 scrolling, 6-7, 12-6, 12-14 simultaneous, 15-12 solving, 7-1, D-1 stack usage, 6-11 storing variable value, 6-11 syntax, 6-13, 6-18, 12-14 TVM equation, 17-1 types of, 6-9 uses - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 378
(angle units), 4-4, A-2 Grandma Hinkle, 11-7 Greatest integer, 4-16 grouped standard deviation, 16-17 GTO, 13-4, 13-17 guesses (for SOLVE), 7-2, 7-5, 7-7, 7-10, 14-6 H help about calculator, A-1 HEX annunciator, 10-1 hex numbers. See numbers arithmetic, 10-2 converting to, 10-1 range of, 10-5 typing - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 379
, 13-20, 13-21, 13-22 INPUT always prompts, 13-10 entering program data, 12-11 in integration programs, 14-8 in SOLVE programs, 14-2 responding to, 12-13 integer-part function, 4-16 integration accuracy, 8-2, 8-5, 8-6, E-1 base mode, 12-22, 14-11 difficult functions, E-2, E-7 display format - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 380
Fraction-display mode, Program-entry mode MODES menu angular mode, 4-4 setting radix, 1-18 money (finance), 17-1 N negative numbers, 1-14, 9-3, 10-4 nested routines, 13-3, 14-11 normal distribution, 16-11 numbers. See binary numbers, hex numbers, octal numbers, variables bases, 10-1, 12-22 changing - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 381
, D-5 polynomials, 12-23, 15-20 population standard deviations, 11-6 power annunciator, 1-1, A-2 power curve fitting, 16-1 power functions, 1-15, 4-2, 9-3 precedence (equation operators), 6-13 precision (numbers), 1-19, 1-21, D-13 present value. See financial calculations PRGM TOP, 12-4, 12-6, 12 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 382
, 12-3 typing name, 1-3 viewing, 12-20 program lines. See programs program names. See program labels program pointer, 12-5, 12-10, 12-17, 12-19, B-3 Program-entry mode, 1-5, 12-5 programs. See program labels ALG operations, 12-4 base mode, 12-22 branching, 13-2, 13-4, 13-6, 13-16 calculations in, 12 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 383
the calculator, A-4, B-2 return (program). See programs Reverse Polish Notation. See RPN rolling the stack, 2-3, C-6 root functions, 4-3 roots. See SOLVE checking, 7-6, D-3 in programs, 14-6 multiple, 7-8 none found, 7-6, D-8 of equations, 7-1 of programs, 14-1 polynomial, 15-20 quadratic, 15 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 384
12-20, B-2 program lengths, 12-20, B-2 prompt digits, 6-13 variable digits, 3-3, 12-13 ®, 13-14 sample standard deviations, 11-6 SCI format. See display format in programs, 12-6 setting, 1-19 scrolling binary numbers, 10-6 equations, 6-7, 12-6, 12-14 seed (random number), 4-14 self-test (calculator - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 385
, 12-11 purpose, 2-1, 2-2 registers, 2-1 reviewing, 2-3, C-6 rolling, 2-3, C-6 separate from variables, 3-2 size limit, 2-4, 9-1 unaffected by VIEW, 12-14 stack lift. See stack default state, B-3 disabling, B-4 enabling, B-4 not affecting, B-4 operation, 2-4 standard deviations calculating, 11-6, 11 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 386
stack, 3-2 showing all digits, 3-3, 12-13 solving for, 7-1, 14-1, 14-6, D-1 storing, 3-2 storing from equation, 6-11 typing name, 1-3 viewing, 3-3, 12-13, 12-16 vectors application program, 15-1 coordinate conversions, 4-11, 9-6, 15-1 operations, 15-1 VIEW displaying program data, 12-13, 12-16, 14 - HP 33s | hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 387
clearing in programs, 12-6 displayed, 2-2 during programs pause, 12-17 exchanging with variables, 3-6 exchanging with Y, 2-4 not clearing, 2-5 part of stack, 2-1 testing, 13-7 unaffected by VIEW, 12-14 Index-15
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 |
 |
hp
33s scientific calculator
user's guide
H
Edition 3
HP part number
F2216-90001