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hp 33s scientific calculatoruser's guideHEdition 3HP part number F2216-90001

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 3November 2004

ContentsPart 1.Basic Operation1. Getting StartedImportant Preliminaries.1–1Turning the Calculator On and Off.1–1Adjusting Display Contrast .1–1Highlights of the Keyboard and Display .1–2Shifted Keys.1–2Alpha Keys.1–3Cursor Keys .1–3Silver Paint Keys .1–4Backspacing and Clearing.1–4Using Menus .1–7Exiting Menus .1–9RPN and ALG Keys .1–10The Display and Annunciators .1–11Keying in Numbers.1–14Making Numbers Negative .1–14Exponents of Ten .1–14Understanding Digit Entry.1–15Range of Numbers and OVERFLOW .1–16Doing Arithmetic .1–16One–Number Functions.1–17Two–Number Functions .1–17Controlling the Display Format .1–18Contents1

Periods and Commas in Numbers. 1–18Number of Decimal Places . 1–19SHOWing Full 12–Digit Precision. 1–20Fractions. 1–21Entering Fractions. 1–21Displaying Fractions . 1–23Messages . 1–23Calculator Memory . 1–24Checking Available Memory . 1–24Clearing All of Memory . 1–242. RPN: The Automatic Memory StackWhat the Stack Is . 2–1The X and Y–Registers are in the Display . 2–2Clearing the X–Register. 2–2Reviewing the Stack. 2–3Exchanging the X– and Y–Registers in the Stack . 2–4Arithmetic – How the Stack Does It . 2–4How ENTER Works . 2–5How CLEAR x Works . 2–6The LAST X Register . 2–7Correcting Mistakes with LAST X. 2–8Reusing Numbers with LAST X. 2–9Chain Calculations in RPN mode . 2–11Work from the Parentheses Out . 2–11Exercises. 2–13Order of Calculation . 2–13More Exercises . 2–142Contents

3. Storing Data into VariablesStoring and Recalling Numbers .3–2Viewing a Variable without Recalling It.3–3Reviewing Variables in the VAR Catalog .3–3Clearing Variables .3–4Arithmetic with Stored Variables .3–4Storage Arithmetic .3–4Recall Arithmetic .3–5Exchanging x with Any Variable.3–6The Variable "i" .3–74. Real–Number FunctionsExponential and Logarithmic Functions .4–1Quotient and Remainder of Division.4–2Power Functions .4–2Trigonometry .4–3Entering π .4–3Setting the Angular Mode.4–4Trigonometric Functions .4–4Hyperbolic Functions.4–6Percentage Functions.4–6Physics Constants .4–8Conversion Functions .4–9Coordinate Conversions .4–10Time Conversions .4–12Angle Conversions.4–13Unit Conversions .4–13Probability Functions.4–14Contents3

Factorial . 4–14Gamma. 4–14Probability . 4–14Parts of Numbers . 4–16Names of Functions. 4–175. FractionsEntering Fractions . 5–1Fractions in the Display. 5–2Display Rules. 5–2Accuracy Indicators. 5–3Longer Fractions. 5–4Changing the Fraction Display. 5–4Setting the Maximum Denominator . 5–5Choosing a Fraction Format. 5–5Examples of Fraction Displays . 5–6Rounding Fractions. 5–7Fractions in Equations. 5–8Fractions in Programs . 5–96. Entering and Evaluating EquationsHow You Can Use Equations . 6–1Summary of Equation Operations. 6–3Entering Equations into the Equation List . 6–4Variables in Equations . 6–4Numbers in Equations . 6–5Functions in Equations. 6–5Parentheses in Equations . 6–6Displaying and Selecting Equations . 6–64Contents

Editing and Clearing Equations .6–7Types of Equations.6–9Evaluating Equations.6–9Using ENTER for Evaluation .6–11Using XEQ for Evaluation .6–12Responding to Equation Prompts .6–12The Syntax of Equations .6–13Operator Precedence.6–13Equation Functions.6–15Syntax Errors .6–18Verifying Equations.6–187. Solving EquationsSolving an Equation.7–1Understanding and Controlling SOLVE .7–5Verifying the Result .7–6Interrupting a SOLVE Calculation .7–7Choosing Initial Guesses for SOLVE.7–7For More Information .7–118. Integrating EquationsIntegrating Equations (³ FN) .8–2Accuracy of Integration .8–5Specifying Accuracy .8–6Interpreting Accuracy .8–6For More Information .8–89. Operations with Complex NumbersThe Complex Stack.9–1Complex Operations .9–2Contents5

Using Complex Numbers in Polar Notation. 9–510. Base Conversions and ArithmeticArithmetic in Bases 2, 8, and 16. 10–2The Representation of Numbers. 10–4Negative Numbers. 10–4Range of Numbers . 10–5Windows for Long Binary Numbers . 10–611. Statistical OperationsEntering Statistical Data . 11–1Entering One–Variable Data. 11–2Entering Two–Variable Data. 11–2Correcting Errors in Data Entry. 11–2Statistical Calculations . 11–4Mean. 11–4Sample Standard Deviation . 11–6Population Standard Deviation . 11–6Linear Regression . 11–7Limitations on Precision of Data. 11–9Summation Values and the Statistics Registers . 11–10Summation Statistics . 11–10The Statistics Registers in Calculator Memory . 11–11Access to the Statistics Registers . 11–11Part 2.Programming12. Simple ProgrammingDesigning a Program . 12–36Contents

Selecting a Mode.12–3Program Boundaries (LBL and RTN) .12–3Using RPN, ALG and Equations in Programs.12–4Data Input and Output .12–4Entering a Program.12–5Keys That Clear.12–6Function Names in Programs.12–7Running a Program.12–9Executing a Program (XEQ).12–9Testing a Program.12–9Entering and Displaying Data . 12–11Using INPUT for Entering Data . 12–11Using VIEW for Displaying Data. 12–13Using Equations to Display Messages . 12–14Displaying Information without Stopping . 12–16Stopping or Interrupting a Program . 12–17Programming a Stop or Pause (STOP, PSE). 12–17Interrupting a Running Program . 12–17Error Stops . 12–17Editing a Program . 12–18Program Memory . 12–19Viewing Program Memory . 12–19Memory Usage . 12–20The Catalog of Programs (MEM). 12–20Clearing One or More Programs . 12–20The Checksum. 12–21Nonprogrammable Functions . 12–22Programming with BASE. 12–22Contents7

Selecting a Base Mode in a Program . 12–22Numbers Entered in Program Lines . 12–23Polynomial Expressions and Horner's Method . 12–2313. Programming TechniquesRoutines in Programs . 13–1Calling Subroutines (XEQ, RTN) . 13–2Nested Subroutines . 13–3Branching (GTO) . 13–4A Programmed GTO Instruction . 13–5Using GTO from the Keyboard . 13–5Conditional Instructions. 13–6Tests of Comparison (x?y, x?0) . 13–7Flags. 13–8Loops. 13–16Conditional Loops (GTO). 13–17Loops with Counters (DSE, ISG) . 13–18Indirectly Addressing Variables and Labels . 13–20The Variable "i". 13–20The Indirect Address, (i) . 13–21Program Control with (i) . 13–22Equations with (i) . 13–2414. Solving and Integrating ProgramsSolving a Program . 14–1Using SOLVE in a Program. 14–6Integrating a Program. 14–7Using Integration in a Program . 14–9Restrictions on Solving and Integrating . 14–118Contents

15. Mathematics ProgramsVector Operations .15–1Solutions of Simultaneous Equations . 15–12Polynomial Root Finder . 15–20Coordinate Transformations . 15–3216. Statistics ProgramsCurve Fitting.16–1Normal and Inverse–Normal Distributions . 16–11Grouped Standard Deviation . 16–1717. Miscellaneous Programs and EquationsTime Value of Money .17–1Prime Number Generator .17–6Part 3.Appendixes and ReferenceA. Support, Batteries, and ServiceCalculator Support . A–1Answers to Common Questions . A–1Environmental Limits. A–2Changing the Batteries. A–2Testing Calculator Operation . A–4The Self–Test. A–5Warranty . A–6Service . A–7Regulatory Information . A–9B. User Memory and the StackManaging Calculator Memory . B–1Contents9

Resetting the Calculator . B–2Clearing Memory . B–3The Status of Stack Lift . B–4Disabling Operations . B–4Neutral Operations . B–4The Status of the LAST X Register . B–6C. ALG: SummaryAbout ALG . C–1Doing Two–number Arithmetic in ALG . C–2Simple Arithmetic . C–2Power Functions . C–2Percentage Calculations . C–3Permutations and Combinations . C–4Quotient and Remainder Of Division. C–4Parentheses Calculations . C–5Chain Calculations . C–5Reviewing the Stack . C–6Coordinate Conversions. C–7Integrating an Equation . C–8Operations with Complex Numbers. C–9Arithmetic in Bases 2, 8, and 16. C–11Entering Statistical Two–Variable Data . C–12D. More about SolvingHow SOLVE Finds a Root . D–1Interpreting Results . D–3When SOLVE Cannot Find a Root . D–8Round–Off Error . D–1310Contents

Underflow .D–14E. More about IntegrationHow the Integral Is Evaluated. E–1Conditions That Could Cause Incorrect Results . E–2Conditions That Prolong Calculation Time . E–7F. MessagesG. Operation IndexIndexContents11

Part 1Basic Operation

1Getting StartedvWatch for this symbol in the margin. It identifiesexamples or keystrokes that are shown in RPNmode and must be performed differently in ALGmode.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 informationyou've 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 Started1–1

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 .1–2Getting Started

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 er foralphabetic 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 Started1–3

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.1–4Getting Started

Keys for ClearingKeybDescriptionBackspace. Keyboard–entry mode:Erases the character immediately to the left of " " (thedigit–entry cursor) or backs out of the current menu. (Menusare described in "Using Menus" on page 1–7.) If thenumber is completed (no cursor), b clears the entirenumber. Equation–entry mode:Erases the character immediately to the left of "¾" (theequation–entry cursor). If a number entry in your equationis complete, b erases the entire number. If the number isnot complete, b erases the character immediately to theleft of " " (the number–entry cursor). " " changes back to"¾" when number entry is complete.b also clears error messages, and deletes the currentprogram line during program entry. Clear or Cancel.Clears the displayed number to zero or cancels the currentsituation (such as a menu, a message, a prompt, a catalog, orEquation–entry or Program–entry mode).Getting Started1–5

Keys for Clearing (continued)Key{cDescriptionThe CLEAR menu ({º} {# } { } { })Contains options for clearing x (the number in the X–register), allvariables, all of memory, or all statistical data.If you select { }, a new menu ( @ {&} { }) isdisplayed so you can verify your decision before erasingeverything in memory.During program entry, { } is replaced by { }. If you select{ }, a new menu ( @ {&} { } ) is displayed, so youcan verify your decision before erasing all your programs.During equation entry (either keyboard equations or equations inprogram lines), the @ {&} { } menu is displayed, so youcan verify your decision before erasing the equation.If you are viewing a completed equation, the equation is deletedwith no verification.1–6Getting Started

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 MenusMenuNameMenuDescriptionChapterNumeric FunctionsL.R.ˆ TPEº̂ Linear regression: curve fitting and linear estimation.11x, yº º·11Arithmetic mean of statistical x– and y–values;weighted mean of statistical x–values.s,σUº U σº σ Sample standard deviation, population standarddeviation.CONSTFunctions to use 40 physics constants—refer to" Physics constants" on page 4–8. SUMSQ ;º ; ;º ; ;º Statistical data summations.11BASE % ! Base conversions (decimal, hexadecimal, octal, andbinary).11114Programming InstructionsFLAGS @Functions to set, clear, and test flags.13x?y Comparison tests of the X–and Y–registers.13x?0 Comparison tests of the X–register and zero.13Getting Started1–7

HP 33s Menus (continued)MenuNameMenuDescriptionChapterOther functio nsMEM# Memory status (bytes of memory available); catalogof variables; catalog of programs (program labels).1, 3, 12MODES * 8Angular modes and ")" or "8" radix (decimal point)convention.4, 1DISPLAY % Fix, scientific, engineering, and ALL display formats.1R¶ R µ% % % % Functions to review the stack in ALG mode –X1–, X2–,X3–, X4–registers CCLEARFunctions to clear different portions of memory—referto { c in the table on page 1–6.1, 3,6, 12To use a menu function:1.Press a menu key (shifted) to produce a menu in the display — a series ofchoices.2. Press select.3. Press to move the underline to the item you want to while the item is underlined.With numbered menu items, you can either pressunderlined, or just enter the number of the item. while the item isThe 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:1–8Getting Started

Example:6 7 0.8571428571 Keys:6Display: % 7 q ({ }) ) ) . ( orMenus help you execute dozens of functions by guiding you to them with menuchoices. You don't 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 b backs out of the 2–level CLEAR or MEM menu, one level at atime. Refer to { c in the table on page 1–6. Pressing b or cancels any other menu.Keys:Display:123.5678 ) % b or ) Pressing another menu key replaces the old menu with the new one.Keys:Display:123.5678 ) % {c % # ) Getting Started1–9

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 mode1 2 ALG mode1 2 In ALG mode, the results and the calculations are displayed. In RPN mode, onlythe results are displayed, not the calculations.Note1–10You can choose either ALG (Algebraic) or RPN (Reverse PolishNotation) mode for your calculations. Throughout the manual, the“v“ in the margin indicates that the examples or keystrokes inRPN mode must be performed differently in ALG mode. AppendixC explains how to use your calculator in ALG mode.Getting Started

The Display and AnnunciatorsFirst LineSecond LineAnnunciatorsThe 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

HP 33s AnnunciatorsAnnunciatorMeaningChapter The " (Busy)" annunciator blinks

hewlett-packard company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability, non-infringement and fitness for a particular purpose. hewlett-packard co. shall not be liable for any errors