hp 33s scientific calculatorusers guideHEdition 3HP part number F2216-90001
NoticeREGISTER YOUR PRODUCT AT: www.register.hp.comTHIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN AREPROVIDED “AS IS” AND A...
ContentsPart 1.        Basic Operation1. Getting Started    Important Preliminaries..........................................
Periods and Commas in Numbers................................ 1–18         Number of Decimal Places .........................
3. Storing Data into Variables    Storing and Recalling Numbers ...........................................3–2    Viewing ...
Factorial .................................................................. 4–14         Gamma..............................
Editing and Clearing Equations ...........................................6–7    Types of Equations..........................
Using Complex Numbers in Polar Notation........................... 9–510. Base Conversions and Arithmetic    Arithmetic in...
Selecting a Mode......................................................12–3     Program Boundaries (LBL and RTN) .............
Selecting a Base Mode in a Program ......................... 12–22         Numbers Entered in Program Lines .................
15. Mathematics Programs    Vector Operations ...........................................................15–1    Solutions...
Resetting the Calculator ..................................................... B–2     Clearing Memory ......................
Underflow ......................................................................D–14E. More about Integration   How the In...
Part 1Basic Operation
1Getting Startedv                 Watch for this symbol in the margin. It identifies                 examples or keystroke...
Highlights of the Keyboard and DisplayShifted KeysEach key has three functions: one printed on its face, a left–shifted fu...
Pressing       or      turns on the corresponding       or     annunciator symbol atthe top of the display. The annunciato...
Silver Paint KeysThose eight silver paint keys have their specific pressure points marked in blueposition in the illustrat...
Keys for ClearingKey                           Description      Backspace.          Keyboard–entry mode:          Erases t...
Keys for Clearing (continued)      Key                                Description              The CLEAR menu ({ } {      ...
Using MenusThere is a lot more power to the HP 33s than what you see on the keyboard. This isbecause 14 of the keys are me...
HP 33s Menus (continued)     Menu                              Menu                               Chapter     Name        ...
Example:6 ÷ 7 = 0.8571428571…Keys:                                        Display:6               7       ({       })( or ...
RPN and ALG KeysThe calculator can be set to perform arithmetic operations in either RPN (ReversePolish Notation) or ALG (...
The Display and Annunciators                                                               First Line                     ...
HP 33s Annunciators  Annunciator                           Meaning                        Chapter                     The ...
HP 33s Annunciators (continued)  Annunciator                       Meaning                            Chapter  ,          ...
Keying in NumbersYou can key in a number that has up to 12 digits plus a 3–digit exponent up to±499. If you try to key in ...
Keying in Exponents of TenUse      (exponent) to key in numbers multiplied by powers of ten. For example,take Plancks cons...
Keys:                 Display:                        Description:123                        _                  Digit entr...
One–Number FunctionsTo use a one–number function (such as        ,    ,     ,                  ,       ,       ,        , ...
For example,      To calculate:                      Press:                 Display:12 + 3                    12          ...
Number of Decimal PlacesAll numbers are stored with 12–digit precision, but you can select the number ofdecimal places to ...
Engineering Format ({            })ENG format displays a number in a manner similar to scientific notation, exceptthat the...
For example, in the number 14.8745632019, you see only "14.8746" when thedisplay mode is set to FIX 4, but the last six di...
2. Key in the fraction numerator and press                 again. The second   separates the numerator from the denominato...
Displaying FractionsPress            to switch between Fraction–display mode and the currentdecimal display mode.         ...
Calculator MemoryThe HP 33s has 31KB of memory in which you can store any combination of data(variables, equations, or pro...
2RPN: The AutomaticMemory StackThis chapter explains how calculations take place in the automatic memory stackin RPN mode....
T      0.0000         "Oldest" number                     Z      0.0000                     Y      0.0000         Displaye...
Reviewing the StackR   (Roll Down)The       (roll down) key lets you review the entire contents of the stack by"rolling" t...
Exchanging the X– and Y–Registers in the StackAnother key that manipulates the stack contents is         (x exchange y). T...
3. The stack drops.         Notice that when the stack lifts, it replaces the contents of the T– (top) register         wi...
Using a Number Twice in a RowYou can use the replicating feature of                to other advantages. To add anumber to ...
During program entry,      deletes the currently–displayed program line and          cancels program entry.      During di...
2. Reusing a number in a calculation.See appendix B for a comprehensive list of the functions that save x in the LAST Xreg...
Example:Suppose you made a mistake while calculating                                 16 × 19 = 304There are three kinds of...
T        t                       t                        t                 Z        z                       z            ...
9.5     15                          _               Speed of light, c.                                                    ...
Now study the following examples. Remember that you need to pressonly to separate sequentially–entered numbers, such as at...
ExercisesCalculate:    (16.3805x 5)                 = 181.0000       0.05Solution:16.3805                 5               ...
This method takes one additional keystroke. Notice that the first intermediate resultis still the innermost parentheses (7...
A Solution:14          12     18          12            9     7Calculate:232 – (13 × 9) + 1/7 = 412.1429A Solution:23     ...
3Storing Data into VariablesThe HP 33s has 31KB of user memory: memory that you can use to store numbers,equations, and pr...
Each black letter is associated with a key and a unique variable. The letter keysare automatically active when needed. (Th...
Viewing a Variable without Recalling ItThe             function shows you the contents of a variable without putting thatn...
Clearing VariablesVariables values are retained by Continuous Memory until you replace them orclear them. Clearing a varia...
A     15                           A       12      Result: 15       3                                                     ...
Keys:             Display:                      Description:1         D                                 Stores the assumed...
A                                    Exchanges contents of the                                               X–register an...
4Real–Number FunctionsThis chapter covers most of the calculators functions that perform computations onreal numbers, incl...
To Calculate:                         Press:            Natural logarithm (base e)            Common logarithm (base 10)  ...
In RPN mode, to calculate a number y raised to a power x, key in y           x,then press      . (For y > 0, x can be any ...
Setting the Angular ModeThe angular mode specifies which unit of measure to assume for angles used intrigonometric functio...
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Official User Manual for the HP33s Scientific calculator, for members of our calculators for surveyors support group on Land Surveyors United http://landsurveyorsunited.com/group/hp48calculators/forum

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Hp33s calculator user_guide

  1. 1. hp 33s scientific calculatorusers guideHEdition 3HP part number F2216-90001
  2. 2. NoticeREGISTER YOUR PRODUCT AT: www.register.hp.comTHIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN AREPROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOUT NOTICE.HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANYKIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOTLIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY,NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE.HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS ORFOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTIONWITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUALOR THE EXAMPLES CONTAINED HEREIN.© Copyright 1988, 1990-1991, 2003 Hewlett-Packard Development Company,L.P. Reproduction, adaptation, or translation of this manual is prohibited withoutprior written permission of Hewlett-Packard Company, except as allowed underthe copyright laws.Hewlett-Packard Company4995 Murphy Canyon Rd,Suite 301San Diego, CA 92123Printing HistoryEdition 3 November 2004
  3. 3. ContentsPart 1. Basic Operation1. 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 Using Menus ..............................................................1–7 Exiting Menus .............................................................1–9 RPN and ALG Keys ...................................................1–10 The Display and Annunciators .....................................1–11 Keying in Numbers..........................................................1–14 Making Numbers Negative ........................................1–14 Exponents of Ten .......................................................1–14 Understanding Digit Entry...........................................1–15 Range of Numbers and OVERFLOW ............................1–16 Doing Arithmetic .............................................................1–16 One–Number Functions..............................................1–17 Two–Number Functions ..............................................1–17 Controlling the Display Format ..........................................1–18 Contents 1
  4. 4. Periods 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 ............................................. 1–242. RPN: The Automatic Memory Stack What the Stack Is ............................................................. 2–1 The X and Y–Registers are in the Display ........................ 2–2 Clearing the X–Register................................................ 2–2 Reviewing the Stack..................................................... 2–3 Exchanging the X– and Y–Registers in the Stack .............. 2–4 Arithmetic – How the Stack Does It ...................................... 2–4 How ENTER Works ..................................................... 2–5 How CLEAR x Works ................................................... 2–6 The LAST X Register ........................................................... 2–7 Correcting Mistakes with LAST X.................................... 2–8 Reusing Numbers with LAST X....................................... 2–9 Chain Calculations in RPN mode ...................................... 2–11 Work from the Parentheses Out ................................... 2–11 Exercises.................................................................. 2–13 Order of Calculation ................................................. 2–13 More Exercises ......................................................... 2–142 Contents
  5. 5. 3. Storing Data into Variables Storing and Recalling Numbers ...........................................3–2 Viewing a Variable without Recalling It.................................3–3 Reviewing Variables in the VAR Catalog ...............................3–3 Clearing Variables ............................................................3–4 Arithmetic with Stored Variables ..........................................3–4 Storage Arithmetic .......................................................3–4 Recall Arithmetic .........................................................3–5 Exchanging x with Any Variable..........................................3–6 The Variable "i" ................................................................3–74. Real–Number Functions Exponential and Logarithmic Functions .................................4–1 Quotient and Remainder of Division.....................................4–2 Power Functions ................................................................4–2 Trigonometry ....................................................................4–3 Entering π ..................................................................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 Contents 3
  6. 6. Factorial .................................................................. 4–14 Gamma................................................................... 4–14 Probability ............................................................... 4–14 Parts of Numbers ............................................................ 4–16 Names of Functions......................................................... 4–175. Fractions Entering Fractions ............................................................. 5–1 Fractions 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 ........................................................ 5–96. Entering and Evaluating Equations How You Can Use Equations .............................................. 6–1 Summary of Equation Operations........................................ 6–3 Entering Equations into the Equation List ............................... 6–4 Variables in Equations ................................................. 6–4 Numbers in Equations ................................................. 6–5 Functions in Equations.................................................. 6–5 Parentheses in Equations .............................................. 6–6 Displaying and Selecting Equations ..................................... 6–64 Contents
  7. 7. Editing and Clearing Equations ...........................................6–7 Types of Equations.............................................................6–9 Evaluating Equations..........................................................6–9 Using ENTER for Evaluation ........................................6–11 Using XEQ for Evaluation ...........................................6–12 Responding to Equation Prompts ..................................6–12 The Syntax of Equations ...................................................6–13 Operator Precedence.................................................6–13 Equation Functions.....................................................6–15 Syntax Errors ............................................................6–18 Verifying Equations..........................................................6–187. 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 .......................................................7–118. Integrating Equations Integrating Equations ( FN) ...............................................8–2 Accuracy of Integration ......................................................8–5 Specifying Accuracy ....................................................8–6 Interpreting Accuracy ...................................................8–6 For More Information .........................................................8–89. Operations with Complex Numbers The Complex Stack............................................................9–1 Complex Operations .........................................................9–2 Contents 5
  8. 8. Using Complex Numbers in Polar Notation........................... 9–510. Base Conversions and Arithmetic Arithmetic in Bases 2, 8, and 16....................................... 10–2 The Representation of Numbers......................................... 10–4 Negative Numbers.................................................... 10–4 Range of Numbers .................................................... 10–5 Windows for Long Binary Numbers ............................. 10–611. Statistical Operations Entering Statistical Data ................................................... 11–1 Entering One–Variable Data....................................... 11–2 Entering Two–Variable Data........................................ 11–2 Correcting 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 Precision of Data......................................... 11–9 Summation Values and the Statistics Registers ................... 11–10 Summation Statistics ................................................ 11–10 The Statistics Registers in Calculator Memory .............. 11–11 Access to the Statistics Registers ................................ 11–11Part 2. Programming12. Simple Programming Designing a Program ...................................................... 12–36 Contents
  9. 9. Selecting a Mode......................................................12–3 Program Boundaries (LBL and RTN) ..............................12–3 Using RPN, ALG and Equations in Programs..................12–4 Data Input and Output ...............................................12–4Entering a Program..........................................................12–5 Keys That Clear.........................................................12–6 Function Names in Programs.......................................12–7Running a Program..........................................................12–9 Executing a Program (XEQ).........................................12–9 Testing a Program......................................................12–9Entering and Displaying Data ......................................... 12–11 Using INPUT for Entering Data .................................. 12–11 Using VIEW for Displaying Data................................ 12–13 Using Equations to Display Messages ......................... 12–14 Displaying Information without Stopping ..................... 12–16Stopping or Interrupting a Program .................................. 12–17 Programming a Stop or Pause (STOP, PSE)................... 12–17 Interrupting a Running Program ................................. 12–17 Error Stops ............................................................. 12–17Editing a Program ......................................................... 12–18Program Memory .......................................................... 12–19 Viewing Program Memory ........................................ 12–19 Memory Usage ....................................................... 12–20 The Catalog of Programs (MEM)................................ 12–20 Clearing One or More Programs ............................... 12–20 The Checksum......................................................... 12–21Nonprogrammable Functions .......................................... 12–22Programming with BASE................................................. 12–22 Contents 7
  10. 10. Selecting a Base Mode in a Program ......................... 12–22 Numbers Entered in Program Lines ............................ 12–23 Polynomial Expressions and Horners Method ................... 12–2313. Programming Techniques Routines in Programs ....................................................... 13–1 Calling Subroutines (XEQ, RTN) .................................. 13–2 Nested Subroutines ................................................... 13–3 Branching (GTO) ............................................................ 13–4 A Programmed GTO Instruction ................................... 13–5 Using GTO from the Keyboard .................................... 13–5 Conditional Instructions.................................................... 13–6 Tests of Comparison (x?y, x?0) ................................... 13–7 Flags....................................................................... 13–8 Loops.......................................................................... 13–16 Conditional Loops (GTO).......................................... 13–17 Loops with Counters (DSE, ISG) ................................. 13–18 Indirectly 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) .................................................... 13–2414. Solving and Integrating Programs Solving a Program .......................................................... 14–1 Using SOLVE in a Program............................................... 14–6 Integrating a Program...................................................... 14–7 Using Integration in a Program ......................................... 14–9 Restrictions on Solving and Integrating ............................. 14–118 Contents
  11. 11. 15. Mathematics Programs Vector Operations ...........................................................15–1 Solutions of Simultaneous Equations ................................. 15–12 Polynomial Root Finder ................................................... 15–20 Coordinate Transformations ............................................ 15–3216. Statistics Programs Curve Fitting...................................................................16–1 Normal and Inverse–Normal Distributions ......................... 16–11 Grouped Standard Deviation .......................................... 16–1717. Miscellaneous Programs and Equations Time Value of Money .......................................................17–1 Prime Number Generator .................................................17–6Part 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...................................................... A–2 Testing Calculator Operation ............................................. A–4 The Self–Test.................................................................... A–5 Warranty ........................................................................ A–6 Service ........................................................................... A–7 Regulatory Information ...................................................... A–9 B. User Memory and the Stack Managing Calculator Memory ............................................ B–1 Contents 9
  12. 12. Resetting the Calculator ..................................................... B–2 Clearing Memory ............................................................. B–3 The Status of Stack Lift ....................................................... B–4 Disabling Operations .................................................. B–4 Neutral Operations ..................................................... B–4 The Status of the LAST X Register ......................................... B–6 C. ALG: Summary About ALG ...................................................................... C–1 Doing Two–number Arithmetic in ALG .................................. C–2 Simple Arithmetic ........................................................ C–2 Power Functions .......................................................... C–2 Percentage Calculations ............................................... C–3 Permutations and Combinations .................................... C–4 Quotient and Remainder Of Division.............................. 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 a Root ................................................... D–1 Interpreting Results ............................................................ D–3 When SOLVE Cannot Find a Root ....................................... D–8 Round–Off Error ............................................................. D–1310 Contents
  13. 13. Underflow ......................................................................D–14E. More about Integration How the Integral Is Evaluated.............................................. E–1 Conditions That Could Cause Incorrect Results ....................... E–2 Conditions That Prolong Calculation Time ............................. E–7F. MessagesG. Operation Index Index Contents 11
  14. 14. Part 1Basic Operation
  15. 15. 1Getting Startedv Watch for this symbol in the margin. It identifies examples or keystrokes that are shown in RPN mode and must be performed differently in ALG mode.Appendix C explains how to use your calculator in ALG mode.Important PreliminariesTurning the Calculator On and OffTo turn the calculator on, press . ON is printed below the key.To turn the calculator off, press . That is, press and release the shiftkey, then press (which has OFF printed in purple above it). Since thecalculator has Continuous Memory, turning it off does not affect any informationyouve stored.To conserve energy, the calculator turns itself off after 10 minutes of no use. If yousee the low–power indicator ( ) in the display, replace the batteries as soon aspossible. See appendix A for instructions.Adjusting Display ContrastDisplay contrast depends on lighting, viewing angle, and the contrast setting. Toincrease or decrease the contrast, hold down the key and press or . Getting Started 1–1
  16. 16. Highlights of the Keyboard and DisplayShifted KeysEach key has three functions: one printed on its face, a left–shifted function(Green), and a right–shifted function (Purple). The shifted function names areprinted 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 thecalculator off, press and release the shift key, then press .1–2 Getting Started
  17. 17. Pressing or turns on the corresponding or annunciator symbol atthe top of the display. The annunciator remains on until you press the next key. Tocancel a shift key (and turn off its annunciator), press the same shift key again.Alpha Keys Left-shifted Right-shifted function function G Letter for alphabetic keyMost keys have a letter written next to them, as shown above. Whenever youneed to type a letter (for example, a variable or a program label), the A..Zannunciator appears in the display, indicating that the alpha keys are"active”.Variables are covered in chapter 3; labels are covered in chapter 12.Cursor KeysNote that the cursor key itself is not actually marked with arrows. To make theexplanations in this manual as easy to understand as possible, we will refer tospecific cursor keys as noted in the illustration below. Getting Started 1–3
  18. 18. Silver Paint KeysThose eight silver paint keys have their specific pressure points marked in blueposition in the illustration below.To use those keys, make sure to press down the corresponding position for thedesired function.Backspacing and ClearingOne 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
  19. 19. Keys for ClearingKey Description Backspace. Keyboard–entry mode: Erases the character immediately to the left of "_" (the digit–entry cursor) or backs out of the current menu. (Menus are described in "Using Menus" on page 1–7.) If the number is completed (no cursor), clears the entire number. Equation–entry mode: Erases the character immediately to the left of " " (the equation–entry cursor). If a number entry in your equation is complete, erases the entire number. If the number is not complete, erases the character immediately to the left of "_" (the number–entry cursor). "_" changes back to " " when number entry is complete. 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
  20. 20. Keys for Clearing (continued) Key Description The CLEAR menu ({ } { }{ } { }) Contains options for clearing x (the number in the X–register), all variables, all of memory, or all statistical data. If you select { }, a new menu ( { } { }) is displayed so you can verify your decision before erasing everything 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 verify your decision before erasing the equation. If you are viewing a completed equation, the equation is deleted with no verification.1–6 Getting Started
  21. 21. Using MenusThere is a lot more power to the HP 33s than what you see on the keyboard. This isbecause 14 of the keys are menu keys. There are 14 menus in all, which providemany more functions, or more options for more functions. HP 33s Menus Menu Menu Chapter Name Description Numeric Functions L.R. ˆ ˆ 11 Linear regression: curve fitting and linear estimation. x, y 11 Arithmetic mean of statistical x– and y–values; weighted mean of statistical x–values. s,σ σ σ 11 Sample standard deviation, population standard deviation. CONST Functions to use 40 physics constants—refer to 4 " Physics constants" on page 4–8. SUMS 11 Statistical data summations. BASE 11 Base conversions (decimal, hexadecimal, octal, and binary). Programming Instructions FLAGS 13 Functions to set, clear, and test flags. x?y ≠≤<>≥= 13 Comparison tests of the X–and Y–registers. x?0 ≠≤<>≥= 13 Comparison tests of the X–register and zero. Getting Started 1–7
  22. 22. HP 33s Menus (continued) Menu Menu Chapter Name Description Other functio ns MEM 1, 3, 12 Memory status (bytes of memory available); catalog of variables; catalog of programs (program labels). MODES 4, 1 Angular modes and " " or " " radix (decimal point) convention. DISPLAY 1 Fix, scientific, engineering, and ALL display formats. R R C Functions to review the stack in ALG mode –X1–, X2–, X3–, X4–registers CLEAR Functions to clear different portions of memory—refer 1, 3, to in the table on page 1–6. 6, 12To use a menu function:1. Press a menu key (shifted) to produce a menu in the display — a series of choices.2. Press to move the underline to the item you want to select.3. Press while the item is underlined.With numbered menu items, you can either press while the item isunderlined, or just enter the number of the item.The CONST and SUMS menu keys have more menu pages, turning on the (or ) annunciator. You can use the cursor keys or press the menu key once to accessthe next menu page.The following example shows you how to use a menu function:1–8 Getting Started
  23. 23. Example:6 ÷ 7 = 0.8571428571…Keys: Display:6 7 ({ })( or )Menus help you execute dozens of functions by guiding you to them with menuchoices. You dont have to remember the names of the functions built into thecalculator nor search through the names printed on its keyboard.Exiting MenusWhenever you execute a menu function, the menu automatically disappears,as in the above example. If you want to leave a menu without executing a function,you have three options: Pressing backs out of the 2–level CLEAR or MEM menu, one level at a time. Refer to in the table on page 1–6. Pressing or cancels any other menu. Keys: Display:123.5678 _ or Pressing another menu key replaces the old menu with the new one. Keys: Display:123.5678 _ Getting Started 1–9
  24. 24. RPN and ALG KeysThe calculator can be set to perform arithmetic operations in either RPN (ReversePolish Notation) or ALG (Algebraic) mode.In Reverse Polish Notation (RPN) mode, the intermediate results of calculations arestored automatically; hence, you do not have to use parentheses.In algebraic (ALG) mode, you perform addition, subtraction, multiplication, anddivision in the traditional way.To select RPN mode:Press to set the calculator to RPN mode. When the calculator is in RPNmode, the RPN annunciator is on.To select ALG mode:Press to set the calculator to ALG mode. When the calculator is in ALGmode, the ALG annunciator is on.Example:Suppose you want to calculate 1 + 2 = 3.In RPN mode, you enter the first number, press the key, enter the secondnumber, and finally press the arithmetic operator key: .In ALG mode, you enter the first number, press , enter the second number, andfinally press the key. RPN mode ALG mode 1 2 1 2In ALG mode, the results and the calculations are displayed. In RPN mode, onlythe results are displayed, not the calculations. Note You can choose either ALG (Algebraic) or RPN (Reverse Polish Notation) mode for your calculations. Throughout the manual, the “v“ in the margin indicates that the examples or keystrokes in RPN mode must be performed differently in ALG mode. Appendix C explains how to use your calculator in ALG mode.1–10 Getting Started
  25. 25. The Display and Annunciators First Line Second Line AnnunciatorsThe display comprises two lines and annunciators.The first line can display up to 255 characters. Entries with more than 14characters will scroll to the left. However, if entries are 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 theresult of a calculation. Every calculation is displayed in up to 14 digits, includingan sign (exponent), and exponent value up to three digits.The symbols on the display, shown in the above figure, are called annunciators.Each one has a special significance when it appears in the display. Getting Started 1–11
  26. 26. HP 33s Annunciators Annunciator 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 " " or " " halves of the " " annunciator will be turned on to indicate whether the displayed numerator is slightly less than or slightly greater than its true value. If neither part of " " is on, the exact value of the fraction is being displayed. Left shift is active. 1 Right shift is active. 1RPN Reverse Polish Notation mode is active. 1, 2ALG Algebraic mode is active. 1, CPRGM Program–entry is active. 12EQN Equation–entry mode is active, or the 6 calculator is evaluating an expression or executing an equation.0 1 2 3 4 Indicates which flags are set (flags 5 13 through 11 have no annunciator.RAD or GRAD Radians or Grad angular mode is set. DEG 4 mode (default) has no annunciator.HEX OCT BIN Indicates the active number base. DEC 10 (base 10, default) has no annunciator.1–12 Getting Started
  27. 27. 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–cursor keys ( , ) to see the rest of an equation or binary number. Both these annunciators may appear simultaneously in the display, indicating that there are more characters to the left and to the right. Press either of the indicated cursor keys ( or ) to see the leading or trailing characters. When an entry or equation has more than one display, you can press or followed by to skip from the current display to the first one. To skip to the last display, press or followed by . In the CONST and SUMS menus, you can press and to access the next menu page. , The and keys are active for 1, 6, 12 stepping through an equation list or program lines.A..Z The alphabetic keys are active. 3 Attention! Indicates a special condition or an 1 error. Battery power is low. A Getting Started 1–13
  28. 28. Keying in NumbersYou can key in a number that has up to 12 digits plus a 3–digit exponent up to±499. If you try to key in a number larger than this, digit entry halts and theannunciator briefly appears.If you make a mistake while keying in a number, press to backspace anddelete the last digit, or press to clear the whole number.Making Numbers NegativeThe key changes the sign of a number. To key 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 TenExponents in the DisplayNumbers with exponents of ten (such as 4.2 × 10–5) are displayed with anpreceding the exponent (such as ).A number whose magnitude is too large or too small for the display format willautomatically be displayed in exponential form.For example, in FIX 4 format for four decimal places, observe the effect of thefollowing keystrokes:Keys: Display: Description:.000062 _ Shows number being entered. Rounds number to fit the display format..000042 Automatically uses scientific notation because otherwise no significant digits would appear.1–14 Getting Started
  29. 29. Keying in Exponents of TenUse (exponent) to key in numbers multiplied by powers of ten. For example,take Plancks constant, 6.6261 × 10–34:1. Key in the mantissa (the non–exponent part) of the number. If the mantissa is negative, press after keying in its digits. Keys: Display:6.6261 _2. Press . Notice that the cursor moves behind the : _3. Key in the exponent. (The largest possible exponent is ±499.) If the exponent is negative, press after you key in the or after you key in the value of the exponent:34 _For a power of ten without a multiplier, such as 1034, just press 34. Thecalculator displays .Other Exponent FunctionsTo calculate an exponent of ten (the base 10 antilogarithm), use . Tocalculate the result of any number raised to a power (exponentiation), use(see chapter 4).Understanding Digit EntryAs you key in a number, the cursor (_) appears in the display. The cursor showsyou where the next digit will go; it therefore indicates that the number is notcomplete. Getting Started 1–15
  30. 30. Keys: Display: Description:123 _ Digit entry not terminated: the number is not complete.If you execute a function to calculate a result, the cursor disappears because thenumber is complete — digit entry has been terminated. Digit entry is terminated.Pressing terminates digit entry. To separate two numbers, key in the firstnumber, press to terminate digit, entry, and then key in the secondnumber123 A completed number.4 Another completed number.If digit entry is not terminated (if the cursor is present), backspaces to erasethe last digit. If digit entry is terminated (no cursor), acts like and clearsthe entire number. Try it!Range of Numbers and OVERFLOWThe smallest number available on the calculator is 1 × 10–499. The largest numberis 9.99999999999 × 10499 (displayed as because of rounding). If a calculation produces a result that exceeds the largest possible number, 9.99999999999 × 10 499 is returned, and the warning message appears. If a calculation produces a result smaller that the smallest possible number, zero is returned. No warning message appears.Doing ArithmeticAll operands (numbers) must be present before you press a function key. (Whenyou press a function key, the calculator immediately executes the functionshown on that key.)All calculations can be simplified into one–number functions and/or two–numberfunctions.1–16 Getting Started
  31. 31. One–Number FunctionsTo use a one–number function (such as , , , , , , , or )1. Key in the number. ( You dont need to press .)2. Press the function key. (For a shifted function, press the appropriate or shift key first.)For example, calculate 1/32 and 148.84 . Then square the last result andchange its sign. Keys: Display: Description:32 _ Operand. Reciprocal of 32.148.84 Square root of 148.84. Square of 12.2. Negation of 148.8400.The one–number functions also include trigonometric, logarithmic, hyperbolic, andparts–of–numbers functions, all of which are discussed in chapter 4.Two–Number FunctionsIn RPN mode, to use a two–number function (such as , , , , , , , , , , or ):1. Key in the first number.2. Press to separate the first number from the 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 in both numbers (separate them by selecting ) before selecting a function key. Getting Started 1–17
  32. 32. For example, To calculate: Press: Display:12 + 3 12 312 – 3 12 312 × 3 12 3123 12 3Percent change from 8 58 to 5The order of entry is important only for non–commutative functions such as , , , , , , , , , . If you type numbers in the wrong order, you can still get the correctanswer (without re–typing them) by pressing to swap the order of thenumbers on the stack. Then press the intended function key. (This is explained indetail in chapter 2 under "Exchanging the X– and Y–Registers in the Stack.")Controlling the Display FormatPeriods and Commas in NumbersTo exchange the periods and commas used for the decimal point (radix mark) anddigit separators in a number:1. Press to display the MODES menu.2. Specify the decimal point (radix mark) by pressing { } or { }. For example, the number one million looks like: if you press { } or if you press { }.1–18 Getting Started
  33. 33. Number of Decimal PlacesAll numbers are stored with 12–digit precision, but you can select the number ofdecimal places to be displayed by pressing (the display menu). Duringsome complicated internal calculations, the calculator uses 15–digit precision forintermediate results. The displayed number is rounded according to the displayformat. The DISPLAY menu gives you four options:Fixed–Decimal Format ({ })FIX format displays a number with up to 11 decimal places (11 digits to the right ofthe " " or " " radix mark) if they fit. After the prompt _, type in the number ofdecimal places to be displayed. For 10 or 11 places, press 0 or 1.For example, in the number , the "7", "0", "8", and "9" are thedecimal digits 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–placesetting will automatically be displayed in scientific format.Scientific Format ({ })SCI format displays a number in scientific notation (one digit before the " " or " "radix mark) with up to 11 decimal places (if they fit) and up to three digits in theexponent. After the prompt, _, type in the number of decimal places to bedisplayed. For 10 or 11 places, press 0 or 1. (The mantissa part of thenumber will always be less than 10.)For example, in the number , the "2", "3", "4", and "6" are thedecimal digits you see when the calculator is set to SCI 4 display mode. The "5"following the "E" is the exponent of 10: 1.2346 × 10 5. Getting Started 1–19
  34. 34. Engineering Format ({ })ENG format displays a number in a manner similar to scientific notation, exceptthat the exponent is a multiple of three (there can be up to three digits before the" " or " " radix mark). This format is most useful for scientific and engineeringcalculations that use units specified in multiples of 103 (such as micro–, milli–, andkilo–units.)After the prompt, _, type in the number of digits you want after the firstsignificant digit. For 10 or 11 places, press 0 or 1.For example, in the number , the "2", "3", "4", and "6" are thesignificant digits after the first significant digit you see when the calculator isset to ENG 4 display mode. The "3" following the " " is the (multiple of 3)exponent of 10: 123.46 x 103.Pressing or will cause the exponent display for the numberbeing displayed to change in multiples of 3.For example, key in the number and pressing will convert thedisplayed value to , which the mantissa n satisfies 1≤ n < 1000 andthe exponent is a multiple of 3. When you press again, the displayed valueis converted to by shifting the decimal point three places to the rightand converting the exponent to the next lower multiple of 3.Key in the number and pressing will convert thedisplayed value to , which the mantissa n satisfies 0.01≤ n < 10 andthe exponent is a multiple of 3. When you press again, thedisplayed value is converted to by shifting the decimal pointthree places to the left and converting the exponent to the next higher multiple of 3.ALL Format ({ })ALL format displays a number as precisely as possible (12 digits maximum). If allthe digits dont fit in the display, the number is automatically displayed in scientificformat.SHOWing Full 12–Digit PrecisionChanging the number of displayed decimal places affects what you see, but itdoes not affect the internal representation of numbers. Any number storedinternally always has 12 digits.1–20 Getting Started
  35. 35. For example, in the number 14.8745632019, you see only "14.8746" when thedisplay mode is set to FIX 4, but the last six digits ("632019") are presentinternally in the calculator.To temporarily display a number in full precision, press . This showsyou the mantissa (but no exponent) of the number for as long as you hold down . Keys: Display: Description: { }4 Displays four decimal places.45 1.3 Four decimal places displayed. { }2 Scientific format: two decimal places and an exponent. { }2 Engineering format. { } All significant digits; trailing zeros dropped. { }4 Four decimal places, no exponent. Reciprocal of 58.5. (hold) Shows full precision until you releaseFractionsThe HP 33s allows you to type in and display fractions, and to perform mathoperations on them. Fractions are real numbers of the form a b/cwhere a, b, and c are integers; 0 ≤ b < c; and the denominator (c) must be in therange 2 through 4095.Entering FractionsFractions can be entered onto the stack at any time:1. Key in the integer part of the number and press . (The first separates the integer part of the number from its fractional part.) Getting Started 1–21
  36. 36. 2. Key in the fraction numerator and press again. The second separates the numerator from the denominator.3. Key in the denominator, then press or a function key to terminate digit entry. The number or result is formatted according to the current display format.The a b/c symbol under the key is a reminder that the key is usedtwice for fraction entry.For example, to enter the fractional number 12 3/8, press these keys: Keys: Display: Description:12 _ Enters the integer part of the number. _ The key is interpreted in the normal manner.3 _ Enters the numerator of the fraction (the number is still displayed in decimal form). _ The calculator interprets the second as a fraction and separates the numerator from denominator.8 _ Appends the denominator of the fraction. Terminates digit entry; displays the number in the current display format.If the number you enter has no integer part (for example, 3/8), just start thenumber without an integer: Keys: 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 Getting Started
  37. 37. Displaying FractionsPress to switch between Fraction–display mode and the currentdecimal 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.Now add 3/4 to the number in the X–register (12 3/8): Keys: Display: Description: 3 4 _ Displays characters as you key them in. Adds the numbers in the X– and Y–registers; displays the result as a fraction. Switches to current decimal display format.Refer to chapter 5, "Fractions," for more information about using fractions.MessagesThe calculator responds to certain conditions or keystrokes by displaying amessage. The symbol comes on to call your attention to the message. To clear a message, press or . To clear a message and perform another function, press any other key.If no message appears but does, you have pressed an inactive key (a key thathas no meaning in the current situation, such as in Binary mode).All displayed messages are explained in appendix F, "Messages". Getting Started 1–23
  38. 38. Calculator MemoryThe HP 33s has 31KB of memory in which you can store any combination of data(variables, equations, or program lines).Checking Available MemoryPressing displays the following menu:Where is the number of bytes of memory available.Pressing the { } menu key displays the catalog of variables (see "ReviewingVariables in the VAR Catalog" in chapter 3). Pressing the { } menu key displaysthe catalog of programs.1. To enter the catalog of variables, press { }; to enter the catalog of programs, press { }.2. To review the catalogs, press or .3. To delete a variable or a program, press while viewing it in its catalog.4. To exit the catalog, press .Clearing All of MemoryClearing all of memory erases all numbers, equations, and programs youvestored. It does not affect mode and format settings. (To clear settings as well asdata, see "Clearing Memory" in appendix B.)To clear all of memory:1. Press { }. You will then see the confirmation prompt { } { }, which safeguards against the unintentional clearing of memory.2. Press { } (yes).1–24 Getting Started
  39. 39. 2RPN: The AutomaticMemory StackThis chapter explains how calculations take place in the automatic memory stackin RPN mode. You do not need to read and understand this material to use thecalculator, but understanding the material will greatly enhance your use of thecalculator, especially when programming.In part 2, "Programming", you will learn how the stack can help you to manipulateand organize data for programs.What the Stack IsAutomatic storage of intermediate results is the reason that the HP 33s easilyprocesses complex calculations, and does so without parentheses. The key toautomatic storage is the automatic, RPN memory stack.HPs operating logic is based on an unambiguous, parentheses–free mathematicallogic known as "Polish Notation," developed by the Polish logician Jan ukasiewicz (1878–1956).While conventional algebraic notation places the operators between the relevantnumbers or variables, ukasiewiczs notation places them before the numbers orvariables. For optimal efficiency of the stack, we have modified that notation tospecify the operators after the numbers. Hence the term Reverse Polish Notation, orRPN.The stack consists of four storage locations, called registers, which are "stacked"on top of each other. These registers — labeled X, Y, Z, and T — store andmanipulate four current numbers. The "oldest" number is stored in the T– (top)register. The stack is the work area for calculations. RPN: The Automatic Memory Stack 2–1
  40. 40. T 0.0000 "Oldest" number Z 0.0000 Y 0.0000 Displayed X 0.0000 DisplayedThe most "recent" number is in the X–register: this is the number you see in thesecond line of the display.In programming, the stack is used to perform calculations, to temporarily storeintermediate results, to pass stored data (variables) among programs andsubroutines, to accept input, and to deliver output.The X and Y–Registers are in the DisplayThe X and Y–Registers are what you see except when a menu, a message, or aprogram line is being displayed. You might have noticed that several functionnames include an x or y.This is no coincidence: these letters refer to the X– and Y–registers. For example, raises ten to the power of the number in the X–register.Clearing the X–RegisterPressing { } always clears the X–register to zero; it is also used toprogram this instruction. The key, in contrast, is context–sensitive. It eitherclears or cancels the current display, depending on the situation: it acts like { } only when the X–register is displayed. also acts like{ } when the X–register is displayed and digit entry is terminated (no cursorpresent). It cancels other displays: menus, labeled numbers, messages, equationentry, and program entry.2–2 RPN: The Automatic Memory Stack
  41. 41. Reviewing the StackR (Roll Down)The (roll down) key lets you review the entire contents of the stack by"rolling" the contents downward, one register at a time. You can see eachnumber when it enters the X–register.Suppose the stack is filled with 1, 2, 3, 4. (press 1 2 3 4)Pressing four times rolls the numbers all the way around and back to wherethey started: T 1 4 3 2 1 Z 2 1 4 3 2 Y 3 2 1 4 3 X 4 3 2 1 4What was in the X–register rotates into the T–register, the contents of the T–registerrotate into the Z–register, etc. Notice that only the contents of the registers arerolled — the registers themselves maintain their positions, and only the X– andY–registers contents are displayed.R (Roll Up)The (roll up) key has a similar function to except that it "rolls" thestack contents upward, one register at a time.The contents of the X–register rotate into the Y–register; what was in the T–registerrotates into the X–register, and so on. T 1 2 3 4 1 Z 2 3 4 1 2 Y 3 4 1 2 3 X 4 1 2 3 4 RPN: The Automatic Memory Stack 2–3
  42. 42. Exchanging the X– and Y–Registers in the StackAnother key that manipulates the stack contents is (x exchange y). This keyswaps the contents of the X– and Y–registers without affecting the rest of the stack.Pressing twice restores the original order of the X– and Y–register contents.The function is used primarily to swap the order of numbers in a calculation.For example, one way to calculate 9 ÷ (13 × 8):Press 13 8 9 .The keystrokes to calculate this expression from left–to–right are:9 13 8 . Note Always make sure that there are no more than four numbers in the stack at any given time — the contents of the T–register (the top register) will be lost whenever a fifth number is entered.Arithmetic – How the Stack Does ItThe contents of the stack move up and down automatically as new numbers enterthe X–register (lifting the stack) and as operators combine two numbers in the X–and Y–registers to produce one new number in the X–register (dropping the stack).Suppose the stack is filled with the numbers 1, 2, 3, and 4. See how the stack dropsand lifts its contents while calculating1. The stack "drops" its contents. The T–(top) register replicates its contents.2. The stack "lifts" its contents. The T–registers contents are lost.2–4 RPN: The Automatic Memory Stack
  43. 43. 3. The stack drops. Notice that when the stack lifts, it replaces the contents of the T– (top) register with the contents of the Z–register, and that the former contents of the T–register are lost. You can see, therefore, that the stacks memory is limited to four numbers. Because of the automatic 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 X–register. See appendix B for lists of functions that disable stack lift.How ENTER WorksYou know that separates two numbers keyed in one after the other. Interms of the stack, how does it do this? Suppose the stack is again filled with 1, 2,3, and 4. Now enter and add two new numbers: 1 lost 2 lost T 1 2 3 3 3 Z 2 3 4 4 3 Y 3 4 5 5 4 X 4 5 5 6 11 1 2 3 41. Lifts the stack.2. Lifts the stack and replicates the X–register.3. Does not lift the stack.4. Drops the stack and replicates the T–register. replicates the contents of the X–register into the Y–register. The nextnumber you key in (or recall) writes over the copy of the first number left in theX–register. The effect is simply to separate two sequentially entered numbers.Y ou can use the replicating effect of to clear the stack quickly: press 0 . All stack registers now contain zero. Note, however,that you dont need to clear the stack before doing calculations. RPN: The Automatic Memory Stack 2–5
  44. 44. Using a Number Twice in a RowYou can use the replicating feature of to other advantages. To add anumber to itself, press .Filling the stack with a constantThe replicating effect of together with the replicating effect of stack drop(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 largewould a population of 100 be at the end of 3 days? Replicates T register T 1.5 1.5 1.5 1.5 1.51.5 Z 1.5 1.5 1.5 1.5 1.5 Y 1.5 1.5 1.5 1.5 1.5 X 1.5 100 100 150 225 337.5 1 2 3 4 51. Fills the stack with the growth rate.2. Keys in the initial population.3. Calculates the population after 1 day.4. Calculates the population after 2 days.5. Calculates the population after 3 days.How CLEAR x WorksClearing the X–register puts a zero in the X–register. The next number you key in(or recall) writes over this zero.There are three ways to clear the contents of the X–register, that is, to clear x:1. Press2. Press3. Press { } (Mainly used during program entry.)Note these exceptions:2–6 RPN: The Automatic Memory Stack
  45. 45. During program entry, deletes the currently–displayed program line and cancels program entry. During digit entry, backspaces over the displayed number. If the display shows a labeled number (such as ), pressing or cancels that display and shows the X–register. When viewing an equation, displays the cursor at the end the equation to allow for editing. During equation entry, backspaces over the displayed equation, one function at a time.For example, if you intended to enter 1 and 3 but mistakenly entered 1 and 2, thisis what you should do to correct your error: T Z Y 1 1 1 1 X 1 1 2 0 3 1 2 3 4 51. Lifts the stack2. Lifts the stack and replicates the X–register.3. Overwrites the X–register.4. Clears x by overwriting it with zero.5. Overwrites x (replaces the zero.)The LAST X RegisterThe LAST X register is a companion to the stack: it holds the number that was in theX–register before the last numeric function was executed. (A numeric function is anoperation that produces a result from another number or numbers, such as .)Pressing returns this value into the X–register.This ability to retrieve the "last x" has two main uses:1. Correcting errors. RPN: The Automatic Memory Stack 2–7
  46. 46. 2. Reusing a number in a calculation.See appendix B for a comprehensive list of the functions that save x in the LAST Xregister.Correcting Mistakes with LAST XWrong One–Number FunctionIf you execute the wrong one–number function, use to retrieve thenumber so you can execute the correct function. (Press first if you want toclear the incorrect result from the stack.)Since and dont cause the stack to drop, you can recover fromthese functions in the same manner as from one–number functions.Example:Suppose that you had just computed ln 4.7839 × (3.879 × 105) and wanted tofind its square root, but pressed by mistake. You dont have to start over! Tofind the correct result, press .Mistakes with Two–number FunctionsIf you make a mistake with a two–number operation, ( , , , , , , , , , , or ),you can correct it by using and the inverse of the two–numberfunction.1. Press to recover the second number (x just before the operation).2. Execute the inverse operation. This returns the number that was originally first. The second number is still in the LAST X register. Then: If you had used the wrong function, press again to restore the original stack contents. Now execute the correct function. If you had used the wrong second number, key in the correct one and execute the function.If you had used the wrong first number, key in the correct first number, press to recover the second number, and execute the function again. (Press first if you want to clear the incorrect result from the stack.)2–8 RPN: The Automatic Memory Stack
  47. 47. Example:Suppose you made a mistake while calculating 16 × 19 = 304There are three kinds of mistakes you could have made: Wrong Mistake: Correction: Calculation:16 19 Wrong function15 19 Wrong first number 1616 18 Wrong second number 19Reusing Numbers with LAST XYou can use to reuse a number (such as a constant) in a calculation.Remember to enter the constant second, just before executing the arithmeticoperation, so that the constant is the last number in the X–register, and thereforecan be saved and retrieved with .Example: 96.704 + 52.3947 Calculate 52.3947 RPN: The Automatic Memory Stack 2–9
  48. 48. T t t t Z z z t 96.704 Y 96.7040 96.7040 z X 96.7040 52.3947 52.3 947 149.0987 LAST X l l 52.3947 T t t Z z t Y 149.0987 z X 52.3947 2.8457 LAST X 52.3947 52.3947 Keys: Display: Description:96.704 Enters first number.52.3947 Intermediate result. Brings back display from before . Final result.Example:Two close stellar neighbors of Earth are Rigel Centaurus (4.3 light–years away)and Sirius (8.7 light–years away). Use c, the speed of light (9.5 × 1015 meters peryear) to convert the distances from the Earth to these stars into meters:To Rigel Centaurus: 4.3 yr × (9.5 × 1015 m/yr).To Sirius: 8.7 yr × (9.5 × 1015 m/yr). Keys: Display: Description:4.3 Light–years to Rigel Centaurus.2–10 RPN: The Automatic Memory Stack
  49. 49. 9.5 15 _ Speed of light, c. Meters to R. Centaurus.8.7 Retrieves c. Meters to Sirius.Chain Calculations in RPN modeIn RPN mode, the automatic lifting and dropping of the stacks contents let youretain intermediate results without storing or reentering them, and without usingparentheses.Work from the Parentheses OutFor example, solve (12 + 3) × 7.If you were working out this problem on paper, you would first calculate theintermediate result of (12 + 3) ... (12 + 3) = 1 5… then you would multiply the intermediate result by 7: (15) × 7 = 105Solve the problem in the same way on the HP 33s, starting inside theparentheses: Keys: Display: Description:12 3 Calculates the intermediate result first.You dont need to press to save this intermediate result beforeproceeding; since it is a calculated result, it is saved automatically. Keys: Display: Description:7 Pressing the function key produces the answer. This result can be used in further calculations. RPN: The Automatic Memory Stack 2–11
  50. 50. Now study the following examples. Remember that you need to pressonly to separate sequentially–entered numbers, such as at the beginning of aproblem The operations themselves ( , , etc.) separate subsequent numbersand save intermediate results. The last result saved is the first one retrieved asneeded to carry out the calculation.Calculate 2 ÷ (3 + 10): Keys: Display: Description:3 10 Calculates (3 + 10) first.2 Puts 2 before 13 so the division is correct: 2 ÷ 13.Calculate 4 ÷ [14 + (7 × 3) – 2] : Keys: Display: Description:7 3 Calculates (7 × 3).14 2 Calculates denominator.4 Puts 4 before 33 in preparation for division. Calculates 4 ÷ 33, the answer.Problems that have multiple parentheses can be solved in the same manner usingthe automatic storage of intermediate results. For example, to solve (3 + 4) × (5 +6) on paper, you would first calculate the quantity (3 + 4). Then you wouldcalculate (5 + 6). Finally, you would multiply the two intermediate results to get theanswer.Work through the problem the same way with the HP 33s, except that you donthave to write down intermediate answers—the calculator remembers them for you. Keys: Display: Description:3 4 First adds (3+4)5 6 Then adds (5+6) Then multiplies the intermediate answers together for the final answer.2–12 RPN: The Automatic Memory Stack
  51. 51. ExercisesCalculate: (16.3805x 5) = 181.0000 0.05Solution:16.3805 5 .05Calculate: [(2 + 3) × (4 + 5)] + [(6 + 7) × (8 + 9)] = 21.5743Solution:2 3 4 5 6 7 8 9Calculate:(10 – 5) ÷ [(17 – 12) × 4] = 0.2500Solution:17 12 4 10 5or10 5 17 12 4Order of CalculationWe recommend solving chain calculations by working from the innermostparentheses outward. However, you can also choose to work problems in aleft–to–right order.For example, you have already calculated: 4 ÷ [14 + (7 × 3) – 2]by starting with the innermost parentheses (7 × 3) and working outward, justas you would with pencil and paper. The keystrokes were 7 3 142 4 .If you work the problem from left–to–right, press4 14 7 3 2 . RPN: The Automatic Memory Stack 2–13
  52. 52. This method takes one additional keystroke. Notice that the first intermediate resultis still the innermost parentheses (7 × 3). The advantage to working a problemleft–to–right is that you dont have to use to reposition operands fornomcommutaiive functions ( and ).However, the first method (starting with the innermost parentheses) is oftenpreferred because: It takes fewer keystrokes. It requires fewer registers in the stack. Note When using the left–to–right method, be sure that no more than four intermediate numbers (or results) will be needed at one time (the stack can hold no more than four numbers).The above example, when solved left–to–right, needed all registers in the stack atone point: Keys: Display: Description:4 14 Saves 4 and 14 as intermediate numbers in the stack.7 3 _ At this point the stack is full with numbers for this calculation. Intermediate result. Intermediate result.2 Intermediate result. Final result.More ExercisesPractice using RPN by working through the following problems:Calculate:(14 + 12) × (18 – 12) ÷ (9 – 7) = 78.00002–14 RPN: The Automatic Memory Stack
  53. 53. A Solution:14 12 18 12 9 7Calculate:232 – (13 × 9) + 1/7 = 412.1429A Solution:23 13 9 7Calculate: (5.4 × 0.8) ÷ (12.5 − 0.73 ) = 0.5961Solution:5.4 .8 .7 3 12.5or5.4 .8 12.5 .7 3Calculate: 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:4 5.2 8.33 7.46 0.32 3.152.75 4.3 1.71 2.01 RPN: The Automatic Memory Stack 2–15
  54. 54. 3Storing Data into VariablesThe 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 remindyou of what is stored there, such as B for bank balance and C for the speed oflight.)1. Cursor prompts for variable.2. Indicates letter keys are active.3. Letter keys. Storing Data into Variables 3–1
  55. 55. Each black letter is associated with a key and a unique variable. The letter keysare automatically active when needed. (The A..Z annunciator in the displayconfirms this.)Note that the variables, X, Y, Z and T are different storage locations from theX–register, Y–register, Z–register, and T–register in the stack.Storing and Recalling NumbersNumbers are stored into and recalled from lettered variables with the (store)and (recall) functions.To store a copy of a displayed number (X–register) to a variable:Press letter–key.To recall a copy of a number from a variable to the display:Press letter–key.Example: Storing Numbers.Store Avogadros number (approximately 6.0221 × 1023 ) in A. Keys: Display: Description:6.0221 23 _ Avogadros number. _ Prompts for variable.A (hold key) Displays function as long as key is held down.(release) Stores a copy of Avogadros number in A. This also terminates digit entry (no cursor present). Clears the number in the display. _ Prompts for variable.A Copies Avogadros number from A the display.3–2 Storing Data into Variables
  56. 56. Viewing a Variable without Recalling ItThe function shows you the contents of a variable without putting thatnumber in the X–register. The display is labeled for the variable, such as:In Fraction–display mode ( ), part of the integer may be dropped. Thiswill be indicated by "…" at the left end of the integer.To see the full mantissa, press . The integer part is the portion to theleft of the radix ( or ). is most often used in programming, but it is useful anytime you want toview a variables value without affecting the contents of t he stack.To cancel the VIEW display, press or once.Reviewing Variables in the VAR CatalogThe (memory) function provides information about memory:where nn,nnn is the number of bytes of available memory.Pressing the { } menu key displays the catalog of variables.Pressing the { } menu key displays the catalog of programs.To review the values at any or all non–zero variables:1. Press {VAR}.2. Press or to move the list and display the desired variable. (Note the annunciators, indicating that the and keys are active. If Fraction–display mode is active, indicator will not be turned on to indicate accuracy.) To see all the significant digits of a number displayed in the { } catalog, press . (If it is a binary number with more than 12 digits, use the and keys to see the rest.)3. To copy a displayed variable from the catalog to the X–register, press .4. To clear a variable to zero, press while it is displayed in the catalog.5. Press to cancel the catalog. Storing Data into Variables 3–3
  57. 57. Clearing VariablesVariables values are retained by Continuous Memory until you replace them orclear them. Clearing a variable stores a zero there; a value of zero takes nomemory.To clear a single variable:Store zero in it: Press 0 variable.To clear selected variables:1. Press { } and use or to display the variable.2. Press .3. Press to cancel the catalog.To clear all variables at once:Press { }.Arithmetic with Stored VariablesStorage arithmetic and recall arithmetic allow you to do calculations with anumber stored in a variable without recalling the variable into the stack. Acalculation uses one number from the X–register and one number from thespecified variable.Storage ArithmeticStorage arithmetic uses , , , or to doarithmetic in the variable itself and to store the result there. It uses the value in theX–register and does not affect the stack.New value of variable = Previous value of variable {+, –, ×, ÷} x.For example, suppose you want to reduce the value in A(15) by the number in theX–register (3, displayed). Press A. Now A = 12, while 3 is still in thedisplay.3–4 Storing Data into Variables
  58. 58. A 15 A 12 Result: 15 3 that is,A x T t T t Z z Z z Y y Y y X 3 X 3Recall ArithmeticRecall arithmetic uses , , , or to doarithmetic in the X–register using a recalled number and to leave the result in thedisplay. Only the X–register is affected.New x = Previous x {+, –, ×, ÷} VariableFor example, suppose you want to divide the number in the X–register (3,displayed) by the value in A(12). Press A. Now x = 0.25, while 12 isstill in A. Recall arithmetic saves memory in programs: using A (oneinstruction) uses half as much memory as A, (two instructions). A 12 A 12 T t T t Z z Z z Y y Y y Result: 3 12 that is, x 12 X 3 X 0.25Example:Suppose the variables D, E, and F contain the values 1, 2, and 3. Use storagearithmetic to add 1 to each of those variables. Storing Data into Variables 3–5
  59. 59. Keys: Display: Description:1 D Stores the assumed values into the2 E variable.3 F1 D Adds1 to D, E, and F. E F D Displays the current value of D. E F Clears the VIEW display; displays X-register again.Suppose the variables D, E, and F contain the values 2, 3, and 4 from the lastexample. Divide 3 by D, multiply it by E, and add F to the result. Keys: Display: Description:3 D Calculates 3 ÷ D. E 3 ÷ D × E. F 3 ÷ D × E + F.Exchanging x with Any VariableThe key allows you to exchange the contents of x (the displayedX –register) with the contents of any variable. Executing this function does notaffect the Y–, Z–, or T–registersExample: Keys: Display: Description:12 A Stores 12 in variable A.3 _ Displays x.3–6 Storing Data into Variables
  60. 60. A Exchanges contents of the X–register and variable A. A Exchanges contents of the X–register and variable A. A 12 A 3 T t T t Z z Z z Y y Y y X 3 X 12The Variable "i"There is a 27th variable that you can access directly — the variable i. The keyis labeled "i", and it means i whenever the A..Z annunciator is on. Although itstores numbers as other variables do, i is special in that it can be used to refer toother variables, including the statistics registers, using the (i) function. This is aprogramming technique called indirect addressing that is covered under"Indirectly Addressing Variables and Labels" in chapter 13. Storing Data into Variables 3–7
  61. 61. 4Real–Number FunctionsThis chapter covers most of the calculators functions that perform computations onreal numbers, including some numeric functions used in programs (such as ABS,the absolute–value function): Exponential and logarithmic functions. Quotient and Remainder of Divisions. Power functions. ( and ) Trigonometric functions. Hyperbolic functions. Percentage functions. Physics constants Conversion functions for coordinates, angles, and units. Probability functions. Parts of numbers (number–altering functions).Arithmetic functions and calculations were covered in chapters 1 and 2. Advancednumeric operations (root–finding, integrating, complex numbers, base conversions,and statistics) are described in later chapters.Exponential and Logarithmic FunctionsPut the number in the display, then execute the function — there is no need to press . Real–Number Functions 4–1
  62. 62. To Calculate: Press: Natural logarithm (base e) Common logarithm (base 10) Natural exponential Common exponential (antilogarithm)Quotient and Remainder of DivisionYou can use and to produce either the quotient orremainder of division operations involving two integers.1. Key in the first integer.2. Press to separate the first number from the second.3. 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 Displays the quotient.58 9 Displays the remainder.Power FunctionsTo calculate the square of a number x, key in x and press .To calculate the square root of a number x, key in x and press .To calculate the cube of a number x, key in x and press .To calculate the cube root of a number x, key in x and press .To calculate a power x of 10, key in x and press .4–2 Real–Number Functions
  63. 63. In RPN mode, to calculate a number y raised to a power x, key in y x,then press . (For y > 0, x can be any number; for y < 0, x must be an oddinteger; for y = 0, x must be positive.) To Calculate: Press: Result: 152 15 10 6 6 54 5 4 2 –1.4 2 1.4 (–1.4) 3 1.4 196 196 3 − 125 125In RPN mode, to calculate a root x of a number y (the xth root of y), key in y x, then press . For y < 0, x must be an integer. To Calculate: Press: Result: 4 625 625 4 −1.4 .37893 .37893 1.4TrigonometryEntering πPress to place the first 12 digits of π into the X–register.(The number displayed depends on the display format.) Because π is a function, itdoesnt need to be separated from another number by .Note that the calculator cannot exactly represent π, since π is an irrational number. Real–Number Functions 4–3
  64. 64. Setting the Angular ModeThe angular mode specifies which unit of measure to assume for angles used intrigonometric functions. The mode does not convert numbers already present (see"Conversion Functions" later in this chapter).360 degrees = 2π radians = 400 gradsTo set an angular mode, press . A menu will be displayed from which youcan select an option. Option Description Annunciator { } Sets Degrees mode (DEG). Uses decimal none degrees, not degrees, minutes, and seconds. { } Sets Radians mode (RAD). RAD { } Sets Grads mode (GRAD). GRADTrigonometric FunctionsWith x in the display: To Calculate: Press: Sine of x. Cosine of x. Tangent of x. Arc sine of x. Arc cosine of x. Arc tangent of x. Note Calculations with the irrational number π cannot be expressed exactly by the 12–digit internal precision of the calculator. This is particularly noticeable in trigonometry. For example, the calculated sin π (radians) is not zero but –2.0676 × 10–13, a very small number close to zero.4–4 Real–Number Functions

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