User manual HP 33S

hp 33s scientific calculator user's guide H Edition 3 HP part number F2216-90001 Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE. HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN. © Copyright 1988, 1990-1991, 2003 Hewlett-Packard Development Company, L.P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company 4995 Murphy Canyon Rd, Suite 301 San Diego, CA 92123 Printing History Edition 3 November 2004 Contents Part 1. Basic Operation 1. Getting Started Important Preliminaries.......................................................1­1 Turning the Calculator On and Off.................................1­1 Adjusting Display Contrast ............................................1­1 Highlights of the Keyboard and Display ...............................1­2 Shifted Keys................................................................1­2 Alpha Keys.................................................................1­3 Cursor Keys ................................................................1­3 Silver Paint Keys ..........................................................1­4 Backspacing and Clearing............................................1­4 Using Menus ..............................................................1­7 Exiting Menus .............................................................1­9 RPN and ALG Keys ...................................................1­10 The Display and Annunciators .....................................1­11 Keying in Numbers..........................................................1­14 Making Numbers Negative ........................................1­14 Exponents of Ten .......................................................1­14 Understanding Digit Entry...........................................1­15 Range of Numbers and OVERFLOW ............................1­16 Doing Arithmetic .............................................................1­16 One­Number Functions..............................................1­17 Two­Number Functions ..............................................1­17 Controlling the Display Format ..........................................1­18 Contents 1 Periods and Commas in Numbers................................ 1­18 Number of Decimal Places ......................................... 1­19 SHOWing Full 12­Digit Precision................................ 1­20 Fractions........................................................................ 1­21 Entering Fractions...................................................... 1­21 Displaying Fractions .................................................. 1­23 Messages ...................................................................... 1­23 Calculator Memory ......................................................... 1­24 Checking Available Memory ...................................... 1­24 Clearing All of Memory ............................................. 1­24 2. RPN: The Automatic Memory Stack What the Stack Is ............................................................. 2­1 The X and Y­Registers are in the Display ........................ 2­2 Clearing the X­Register................................................ 2­2 Reviewing the Stack..................................................... 2­3 Exchanging the X­ and Y­Registers in the Stack .............. 2­4 Arithmetic ­ How the Stack Does It ...................................... 2­4 How ENTER Works ..................................................... 2­5 How CLEAR x Works ................................................... 2­6 The LAST X Register ........................................................... 2­7 Correcting Mistakes with LAST X.................................... 2­8 Reusing Numbers with LAST X....................................... 2­9 Chain Calculations in RPN mode ...................................... 2­11 Work from the Parentheses Out ................................... 2­11 Exercises.................................................................. 2­13 Order of Calculation ................................................. 2­13 More Exercises ......................................................... 2­14 2 Contents 3. Storing Data into Variables Storing and Recalling Numbers ...........................................3­2 Viewing a Variable without Recalling It.................................3­3 Reviewing Variables in the VAR Catalog ...............................3­3 Clearing Variables ............................................................3­4 Arithmetic with Stored Variables ..........................................3­4 Storage Arithmetic .......................................................3­4 Recall Arithmetic .........................................................3­5 Exchanging x with Any Variable..........................................3­6 The Variable "i" ................................................................3­7 4. Real­Number Functions Exponential and Logarithmic Functions .................................4­1 Quotient and Remainder of Division.....................................4­2 Power Functions ................................................................4­2 Trigonometry ....................................................................4­3 Entering ..................................................................4­3 Setting the Angular Mode.............................................4­4 Trigonometric Functions ................................................4­4 Hyperbolic Functions..........................................................4­6 Percentage Functions..........................................................4­6 Physics Constants ..............................................................4­8 Conversion Functions .........................................................4­9 Coordinate Conversions .............................................4­10 Time Conversions ......................................................4­12 Angle Conversions.....................................................4­13 Unit Conversions .......................................................4­13 Probability Functions........................................................4­14 Contents 3 Factorial .................................................................. 4­14 Gamma................................................................... 4­14 Probability ............................................................... 4­14 Parts of Numbers ............................................................ 4­16 Names of Functions......................................................... 4­17 5. Fractions Entering Fractions ............................................................. 5­1 Fractions in the Display...................................................... 5­2 Display Rules.............................................................. 5­2 Accuracy Indicators..................................................... 5­3 Longer Fractions.......................................................... 5­4 Changing the Fraction Display............................................ 5­4 Setting the Maximum Denominator ................................ 5­5 Choosing a Fraction Format.......................................... 5­5 Examples of Fraction Displays ....................................... 5­6 Rounding Fractions............................................................ 5­7 Fractions in Equations........................................................ 5­8 Fractions in Programs ........................................................ 5­9 6. Entering and Evaluating Equations How You Can Use Equations .............................................. 6­1 Summary of Equation Operations........................................ 6­3 Entering Equations into the Equation List ............................... 6­4 Variables in Equations ................................................. 6­4 Numbers in Equations ................................................. 6­5 Functions in Equations.................................................. 6­5 Parentheses in Equations .............................................. 6­6 Displaying and Selecting Equations ..................................... 6­6 4 Contents Editing and Clearing Equations ...........................................6­7 Types of Equations.............................................................6­9 Evaluating Equations..........................................................6­9 Using ENTER for Evaluation ........................................6­11 Using XEQ for Evaluation ...........................................6­12 Responding to Equation Prompts ..................................6­12 The Syntax of Equations ...................................................6­13 Operator Precedence.................................................6­13 Equation Functions.....................................................6­15 Syntax Errors ............................................................6­18 Verifying Equations..........................................................6­18 7. Solving Equations Solving an Equation...........................................................7­1 Understanding and Controlling SOLVE .................................7­5 Verifying the Result ......................................................7­6 Interrupting a SOLVE Calculation ...................................7­7 Choosing Initial Guesses for SOLVE................................7­7 For More Information .......................................................7­11 8. Integrating Equations Integrating Equations ( FN) ...............................................8­2 Accuracy of Integration ......................................................8­5 Specifying Accuracy ....................................................8­6 Interpreting Accuracy ...................................................8­6 For More Information .........................................................8­8 9. Operations with Complex Numbers The Complex Stack............................................................9­1 Complex Operations .........................................................9­2 Contents 5 Using Complex Numbers in Polar Notation........................... 9­5 10. Base Conversions and Arithmetic Arithmetic in Bases 2, 8, and 16....................................... 10­2 The Representation of Numbers......................................... 10­4 Negative Numbers.................................................... 10­4 Range of Numbers .................................................... 10­5 Windows for Long Binary Numbers ............................. 10­6 11. Statistical Operations Entering Statistical Data ................................................... 11­1 Entering One­Variable Data....................................... 11­2 Entering Two­Variable Data........................................ 11­2 Correcting Errors in Data Entry.................................... 11­2 Statistical Calculations ..................................................... 11­4 Mean...................................................................... 11­4 Sample Standard Deviation ........................................ 11­6 Population Standard Deviation .................................... 11­6 Linear Regression ...................................................... 11­7 Limitations on Precision of Data......................................... 11­9 Summation Values and the Statistics Registers ................... 11­10 Summation Statistics ................................................ 11­10 The Statistics Registers in Calculator Memory .............. 11­11 Access to the Statistics Registers ................................ 11­11 Part 2. Programming 12. Simple Programming Designing a Program ...................................................... 12­3 6 Contents Selecting a Mode......................................................12­3 Program Boundaries (LBL and RTN) ..............................12­3 Using RPN, ALG and Equations in Programs..................12­4 Data Input and Output ...............................................12­4 Entering a Program..........................................................12­5 Keys That Clear.........................................................12­6 Function Names in Programs.......................................12­7 Running a Program..........................................................12­9 Executing a Program (XEQ).........................................12­9 Testing a Program......................................................12­9 Entering and Displaying Data ......................................... 12­11 Using INPUT for Entering Data .................................. 12­11 Using VIEW for Displaying Data................................ 12­13 Using Equations to Display Messages ......................... 12­14 Displaying Information without Stopping ..................... 12­16 Stopping or Interrupting a Program .................................. 12­17 Programming a Stop or Pause (STOP, PSE)................... 12­17 Interrupting a Running Program ................................. 12­17 Error Stops ............................................................. 12­17 Editing a Program ......................................................... 12­18 Program Memory .......................................................... 12­19 Viewing Program Memory ........................................ 12­19 Memory Usage ....................................................... 12­20 The Catalog of Programs (MEM)................................ 12­20 Clearing One or More Programs ............................... 12­20 The Checksum......................................................... 12­21 Nonprogrammable Functions .......................................... 12­22 Programming with BASE................................................. 12­22 Contents 7 Selecting a Base Mode in a Program ......................... 12­22 Numbers Entered in Program Lines ............................ 12­23 Polynomial Expressions and Horner's Method ................... 12­23 13. Programming Techniques Routines in Programs ....................................................... 13­1 Calling Subroutines (XEQ, RTN) .................................. 13­2 Nested Subroutines ................................................... 13­3 Branching (GTO) ............................................................ 13­4 A Programmed GTO Instruction ................................... 13­5 Using GTO from the Keyboard .................................... 13­5 Conditional Instructions.................................................... 13­6 Tests of Comparison (x?y, x?0) ................................... 13­7 Flags....................................................................... 13­8 Loops.......................................................................... 13­16 Conditional Loops (GTO).......................................... 13­17 Loops with Counters (DSE, ISG) ................................. 13­18 Indirectly Addressing Variables and Labels ....................... 13­20 The Variable "i"...................................................... 13­20 The Indirect Address, (i) ........................................... 13­21 Program Control with (i) ........................................... 13­22 Equations with (i) .................................................... 13­24 14. Solving and Integrating Programs Solving a Program .......................................................... 14­1 Using SOLVE in a Program............................................... 14­6 Integrating a Program...................................................... 14­7 Using Integration in a Program ......................................... 14­9 Restrictions on Solving and Integrating ............................. 14­11 8 Contents 15. Mathematics Programs Vector Operations ...........................................................15­1 Solutions of Simultaneous Equations ................................. 15­12 Polynomial Root Finder ................................................... 15­20 Coordinate Transformations ............................................ 15­32 16. Statistics Programs Curve Fitting...................................................................16­1 Normal and Inverse­Normal Distributions ......................... 16­11 Grouped Standard Deviation .......................................... 16­17 17. Miscellaneous Programs and Equations Time Value of Money .......................................................17­1 Prime Number Generator .................................................17­6 Part 3. Appendixes and Reference A. Support, Batteries, and Service Calculator Support ........................................................... A­1 Answers to Common Questions .................................... A­1 Environmental Limits.......................................................... A­2 Changing the Batteries...................................................... A­2 Testing Calculator Operation ............................................. A­4 The Self­Test.................................................................... A­5 Warranty ........................................................................ A­6 Service ........................................................................... A­7 Regulatory Information ...................................................... A­9 B. User Memory and the Stack Managing Calculator Memory ............................................ B­1 Contents 9 Resetting the Calculator ..................................................... B­2 Clearing Memory ............................................................. B­3 The Status of Stack Lift ....................................................... B­4 Disabling Operations .................................................. B­4 Neutral Operations ..................................................... B­4 The Status of the LAST X Register ......................................... B­6 C. ALG: Summary About ALG ...................................................................... C­1 Doing Two­number Arithmetic in ALG .................................. C­2 Simple Arithmetic ........................................................ C­2 Power Functions .......................................................... C­2 Percentage Calculations ............................................... C­3 Permutations and Combinations .................................... C­4 Quotient and Remainder Of Division.............................. C­4 Parentheses Calculations .................................................... C­5 Chain Calculations ........................................................... C­5 Reviewing the Stack .......................................................... C­6 Coordinate Conversions..................................................... C­7 Integrating an Equation ..................................................... C­8 Operations with Complex Numbers..................................... C­9 Arithmetic in Bases 2, 8, and 16....................................... C­11 Entering Statistical Two­Variable Data ............................... C­12 D. More about Solving How SOLVE Finds a Root ................................................... D­1 Interpreting Results ............................................................ D­3 When SOLVE Cannot Find a Root ....................................... D­8 Round­Off Error ............................................................. D­13 10 Contents Underflow ......................................................................D­14 E. More about Integration How the Integral Is Evaluated.............................................. E­1 Conditions That Could Cause Incorrect Results ....................... E­2 Conditions That Prolong Calculation Time ............................. E­7 F. Messages G. Operation Index Index Contents 11 Part 1 Basic Operation 1 Getting Started v 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 Preliminaries Turning the Calculator On and Off To turn the calculator on, press . ON is printed below the key. . That is, press and release the shift To turn the calculator off, press (which has OFF printed in purple above it). Since the key, then press calculator has Continuous Memory, turning it off does not affect any information you've stored. To conserve energy, the calculator turns itself off after 10 minutes of no use. If you ) in the display, replace the batteries as soon as see the low­power indicator ( possible. See appendix A for instructions. Adjusting Display Contrast Display contrast depends on lighting, viewing angle, and the contrast setting. To increase or decrease the contrast, hold down the key and press or . Getting Started 1­1 Highlights of the Keyboard and Display Shifted Keys Each key has three functions: one printed on its face, a left­shifted function (Green), and a right­shifted function (Purple). The shifted function names are printed in green and purple above each key. Press the appropriate shift key ( or ) before pressing the key for the desired function. For example, to turn the calculator off, press and release the shift key, then press . 1­2 Getting Started Pressing or turns on the corresponding or annunciator symbol at the top of the display. The annunciator remains on until you press the next key. To cancel a shift key (and turn off its annunciator), press the same shift key again. Alpha Keys Left-shifted function Right-shifted function G Letter for alphabetic key Most keys have a letter written next to them, as shown above. Whenever you need to type a letter (for example, a variable or a program label), the A..Z annunciator appears in the display, indicating that the alpha keys are "active". Variables are covered in chapter 3; labels are covered in chapter 12. Cursor Keys Note that the cursor key itself is not actually marked with arrows. To make the explanations in this manual as easy to understand as possible, we will refer to specific cursor keys as noted in the illustration below. Getting Started 1­3 Silver Paint Keys Those eight silver paint keys have their specific pressure points marked in blue position in the illustration below. To use those keys, make sure to press down the corresponding position for the desired function. Backspacing and Clearing One of the first things you need to know is how to clear: how to correct numbers, clear the display, or start over. 1­4 Getting Started Keys for Clearing Key Backspace. Keyboard­entry mode: Erases the character immediately to the left of "_" (the digit­entry cursor) or backs out of the current menu. (Menus are described in "Using Menus" on page 1­7.) If the number is completed (no cursor), clears the entire number. Equation­entry mode: Erases the character immediately to the left of " " (the equation­entry cursor). If a number entry in your equation erases the entire number. If the number is is complete, not complete, erases the character immediately to the left of "_" (the number­entry 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 Equation­entry or Program­entry mode). Description Getting Started 1­5 Keys for Clearing (continued) Key Description The CLEAR menu ({ } { }{ } { }) Contains options for clearing x (the number in the X­register), 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. 1­6 Getting Started Using Menus There is a lot more power to the HP 33s than what you see on the keyboard. This is because 14 of the keys are menu keys. There are 14 menus in all, which provide many more functions, or more options for more functions. HP 33s Menus Menu Name L.R. Menu Description Numeric Functions Chapter ^^ Linear regression: curve fitting and linear estimation. Arithmetic mean of statistical x­ and y­values; weighted mean of statistical x­values. 11 11 x, y s, Sample standard deviation, population standard deviation. Functions to use 40 physics constants--refer to " Physics constants" on page 4­8. Statistical data summations. BASE Base conversions (decimal, hexadecimal, octal, and binary). 11 CONST SUMS 4 11 11 Programming Instructions FLAGS Functions to set, clear, and test flags. x?y x?0 <>= Comparison tests of the X­and Y­registers. <>= Comparison tests of the X­register and zero. 13 13 13 Getting Started 1­7 HP 33s Menus (continued) Menu Name MEM Memory status (bytes of memory available); catalog of variables; catalog of programs (program labels). MODES Angular modes and " " or " " radix (decimal point) convention. DISPLAY Fix, scientific, engineering, and ALL display formats. R R Functions to review the stack in ALG mode ­X1­, X2­, X3­, X4­registers CLEAR Functions to clear different portions of memory--refer to in the table on page 1­6. 1, 3, 6, 12 C 1 4, 1 Menu Description Other functio ns Chapter 1, 3, 12 To use a menu function: 1. Press a menu key (shifted) to produce a menu in the display -- a series of choices. to move the underline to the item you want to while the item is underlined. while the item is 2. Press select. 3. Press With numbered menu items, you can either press underlined, or just enter the number of the item. (or The CONST and SUMS menu keys have more menu pages, turning on the ) annunciator. You can use the cursor keys or press the menu key once to access the next menu page. The following example shows you how to use a menu function: 1­8 Getting Started Example: 6 ÷ 7 = 0.8571428571... Keys: 6 ({ ( or 7 }) ) Display: Menus help you execute dozens of functions by guiding you to them with menu choices. You don't have to remember the names of the functions built into the calculator nor search through the names printed on its keyboard. Exiting Menus Whenever 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 2­level CLEAR or MEM menu, one level at a time. Refer to in the table on page 1­6. Pressing or cancels any other menu. Keys: 123.5678 _ Display: or Pressing another menu key replaces the old menu with the new one. Keys: 123.5678 _ Display: Getting Started 1­9 RPN and ALG Keys The calculator can be set to perform arithmetic operations in either RPN (Reverse Polish Notation) or ALG (Algebraic) mode. In Reverse Polish Notation (RPN) mode, the intermediate results of calculations are stored automatically; hence, you do not have to use parentheses. In algebraic (ALG) mode, you perform addition, subtraction, multiplication, and division in the traditional way. To select RPN mode: to set the calculator to RPN mode. When the calculator is in RPN Press mode, the RPN annunciator is on. To select ALG mode: to set the calculator to ALG mode. When the calculator is in ALG Press mode, the ALG annunciator is on. Example: Suppose you want to calculate 1 + 2 = 3. In RPN mode, you enter the first number, press the number, and finally press the arithmetic operator key: In ALG mode, you enter the first number, press key. finally press the key, enter the second . , enter the second number, and RPN mode 1 2 1 ALG mode 2 In ALG mode, the results and the calculations are displayed. In RPN mode, only the results are displayed, not the calculations. Note You can choose either ALG (Algebraic) or 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. 1­10 Getting Started The Display and Annunciators First Line Second Line Annunciators The display comprises two lines and annunciators. The first line can display up to 255 characters. Entries with more than 14 characters 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 the result of a calculation. Every calculation is displayed in up to 14 digits, including an 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 1­11 HP 33s Annunciators Annunciator Meaning The " (Busy)" annunciator blinks while an operation, equation, or program is executing. When in Fraction­display mode (press ), 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. Right shift is active. RPN ALG PRGM EQN Reverse Polish Notation mode is active. Algebraic mode is active. Program­entry is active. Equation­entry mode is active, or the calculator is evaluating an expression or executing an equation. Indicates which flags are set (flags 5 through 11 have no annunciator. Radians or Grad angular mode is set. DEG mode (default) has no annunciator. Indicates the active number base. DEC (base 10, default) has no annunciator. 5 Chapter 1 1 1, 2 1, C 12 6 01234 RAD or GRAD HEX OCT BIN 13 4 10 1­12 Getting Started HP 33s Annunciators (continued) Annunciator , Meaning The or keys are active to scroll the display, i.e. there are more digits to the left and right. (Equation­entry and Program­entry mode aren't included) Use to see the rest of a decimal number; use the left and right­cursor 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. Chapter 1, 6 , The and keys are active for stepping through an equation list or program lines. The alphabetic keys are active. Attention! Indicates a special condition or an error. Battery power is low. 1, 6, 12 A..Z 3 1 A Getting Started 1­13 Keying in Numbers You can key in a number that has up to 12 digits plus a 3­digit exponent up to ±499. If you try to key in a number larger than this, digit entry halts and the annunciator briefly appears. If you make a mistake while keying in a number, press delete the last digit, or press to clear the whole number. to backspace and Making Numbers Negative The 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 non­exponent part of the number.) Exponents of Ten Exponents in the Display Numbers with exponents of ten (such as 4.2 × 10­5) are displayed with an preceding the exponent (such as ). A number whose magnitude is too large or too small for the display format will automatically be displayed in exponential form. For example, in FIX 4 format for four decimal places, observe the effect of the following keystrokes: Keys: .000062 Display: _ Description: Shows number being entered. Rounds number to fit the display format. .000042 Automatically uses scientific notation because otherwise no significant digits would appear. 1­14 Getting Started Keying in Exponents of Ten (exponent) to key in numbers multiplied by powers of ten. For example, Use take Planck's constant, 6.6261 × 10­34: 1. Key in the mantissa (the non­exponent part) of the number. If the mantissa is negative, press after keying in its digits. Keys: 6.6261 2. Press Display: _ . Notice that the cursor moves behind the : _ 3. Key in the exponent. (The largest possible exponent is ±499.) If the exponent is after you key in the or after you key in the value of the negative, press exponent: 34 _ For a power of ten without a multiplier, such as 1034, just press calculator displays . Other Exponent Functions 34. The . To To calculate an exponent of ten (the base 10 antilogarithm), use calculate the result of any number raised to a power (exponentiation), use (see chapter 4). Understanding Digit Entry As you key in a number, the cursor (_) appears in the display. The cursor shows you where the next digit will go; it therefore indicates that the number is not complete. Getting Started 1­15 Keys: 123 Display: _ Description: Digit entry not terminated: the number is not complete. If you execute a function to calculate a result, the cursor disappears because the number is complete -- digit entry has been terminated. Digit entry is terminated. Pressing number, press number 123 4 terminates digit entry. To separate two numbers, key in the first to terminate digit, entry, and then key in the second A completed number. Another completed number. backspaces to erase acts like and clears If digit entry is not terminated (if the cursor is present), the last digit. If digit entry is terminated (no cursor), the entire number. Try it! Range of Numbers and OVERFLOW The smallest number available on the calculator is 1 × 10­499. The largest number is 9.99999999999 × 10499 (displayed as because of rounding). If a calculation produces a result that exceeds the largest possible number, 9.99999999999 × 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 Arithmetic All operands (numbers) must be present before you press a function key. (When you press a function key, the calculator immediately executes the function shown on that key.) All calculations can be simplified into one­number functions and/or two­number functions. 1­16 Getting Started One­Number Functions To use a one­number function (such as , , or ) 1. , , , .) or , , Key in the number. ( You don't need to press 2. Press the function key. (For a shifted function, press the appropriate shift key first.) For example, calculate 1/32 and change its sign. 148.84 . Then square the last result and Description: Operand. Reciprocal of 32. Square root of 148.84. Square of 12.2. Negation of 148.8400. Keys: 32 148.84 Display: _ The one­number functions also include trigonometric, logarithmic, hyperbolic, and parts­of­numbers functions, all of which are discussed in chapter 4. Two­Number Functions In RPN mode, to use a two­number function (such as , , , , , 1. Key in the first number. to separate the first number from the second. .) 2. Press , or , , , ): , 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 1­17 For example, To calculate: 12 + 3 12 ­ 3 12 × 3 123 Percent change from 8 to 5 12 12 12 12 8 Press: 3 3 3 3 5 Display: , The order of entry is important only for non­commutative functions such as , , , , , , , , . If you type numbers in the wrong order, you can still get the correct answer (without re­typing them) by pressing to swap the order of the numbers on the stack. Then press the intended function key. (This is explained in detail in chapter 2 under "Exchanging the X­ and Y­Registers in the Stack.") Controlling the Display Format Periods and Commas in Numbers To exchange the periods and commas used for the decimal point (radix mark) and digit 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 { }. 1­18 Getting Started Number of Decimal Places All numbers are stored with 12­digit precision, but you can select the number of decimal places to be displayed by pressing (the display menu). During some complicated internal calculations, the calculator uses 15­digit precision for intermediate results. The displayed number is rounded according to the display format. The DISPLAY menu gives you four options: Fixed­Decimal Format ({ }) FIX format displays a number with up to 11 decimal places (11 digits to the right of the " " or " " radix mark) if they fit. After the prompt _, type in the number of 0 or 1. decimal places to be displayed. For 10 or 11 places, press For example, in the number , the "7", "0", "8", and "9" are the decimal 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 decimal­place setting 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 the exponent. After the prompt, _, type in the number of decimal places to be 0 or 1. (The mantissa part of the displayed. For 10 or 11 places, press number will always be less than 10.) , the "2", "3", "4", and "6" are the For example, in the number decimal 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 1­19 Engineering Format ({ }) ENG format displays a number in a manner similar to scientific notation, except that 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 engineering calculations that use units specified in multiples of 103 (such as micro­, milli­, and kilo­units.) After the prompt, _, type in the number of digits you want after the first 0 or 1. significant digit. For 10 or 11 places, press , the "2", "3", "4", and "6" are the For example, in the number significant digits after the first significant digit you see when the calculator is set to ENG 4 display mode. The "3" following the " " is the (multiple of 3) exponent of 10: 123.46 x 103. or will cause the exponent display for the number Pressing being displayed to change in multiples of 3. and pressing will convert the For example, key in the number , which the mantissa n satisfies 1 n < 1000 and displayed value to the exponent is a multiple of 3. When you press again, the displayed value by shifting the decimal point three places to the right is converted to and converting the exponent to the next lower multiple of 3. and pressing will convert the Key in the number , which the mantissa n satisfies 0.01 n < 10 and displayed value to the exponent is a multiple of 3. When you press again, the by shifting the decimal point displayed value is converted to three 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 all the digits don't fit in the display, the number is automatically displayed in scientific format. SHOWing Full 12­Digit Precision Changing the number of displayed decimal places affects what you see, but it does not affect the internal representation of numbers. Any number stored internally always has 12 digits. 1­20 Getting Started For example, in the number 14.8745632019, you see only "14.8746" when the display mode is set to FIX 4, but the last six digits ("632019") are present internally in the calculator. . This shows To temporarily display a number in full precision, press you the mantissa (but no exponent) of the number for as long as you hold down . Keys: { 45 { { { { }4 1.3 }2 }2 } }4 Display: Description: Displays four decimal places. Four decimal places displayed. Scientific format: two decimal places and an exponent. Engineering format. All significant digits; trailing zeros dropped. Four decimal places, no exponent. Reciprocal of 58.5. Shows full precision until you release (hold) Fractions The HP 33s allows you to type in and display fractions, and to perform math operations on them. Fractions are real numbers of the form a b/c where a, b, and c are integers; 0 b < c; and the denominator (c) must be in the range 2 through 4095. Entering Fractions Fractions can be entered onto the stack at any time: 1. . (The first Key in the integer part of the number and press separates the integer part of the number from its fractional part.) Getting Started 1­21 2. Key in the fraction numerator and press separates the numerator from the denominator. again. The second or a function key to terminate 3. Key in the denominator, then press digit entry. The number or result is formatted according to the current display format. The a b/c symbol under the twice for fraction entry. key is a reminder that the key is used For example, to enter the fractional number 12 3/8, press these keys: Keys: 12 Display: _ _ Description: 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. _ Appends the denominator of the fraction. Terminates digit entry; displays the number in the current display format. _ 8 If the number you enter has no integer part (for example, 3/8), just start the number without an integer: Keys: 3 8 Display: _ Description: Enters no integer part. (3 also works.) 8 Terminates digit entry; displays the number in the current display format (FIX 4). 1­22 Getting Started Displaying Fractions Press to switch between Fraction­display mode and the current decimal display mode. Keys: 12 3 8 Display: _ Description: Displays characters as you key them in. Terminates digit entry; displays the number in the current display format. Displays the number as a fraction. Now add 3/4 to the number in the X­register (12 3/8): Keys: 3 4 Display: _ Description: Displays characters as you key them in. Adds the numbers in the X­ and Y­registers; displays the result as a fraction. Switches to current decimal display format. Refer to chapter 5, "Fractions," for more information about using fractions. Messages The calculator responds to certain conditions or keystrokes by displaying a message. The symbol comes on to call your attention to the message. To clear a message, press or . To clear a message and perform another function, press any other key. does, you have pressed an inactive key (a key that If no message appears but has no meaning in the current situation, such as in Binary mode). All displayed messages are explained in appendix F, "Messages". Getting Started 1­23 Calculator Memory The HP 33s has 31KB of memory in which you can store any combination of data (variables, equations, or program lines). Checking Available Memory Pressing displays the following menu: Where is the number of bytes of memory available. Pressing the { } menu key displays the catalog of variables (see "Reviewing Variables in the VAR Catalog" in chapter 3). Pressing the { } menu key displays the catalog of programs. 1. To enter the catalog of variables, press { press { }. 2. To review the catalogs, press or 3. To delete a variable or a program, press catalog. 4. To exit the catalog, press . }; to enter the catalog of programs, . while viewing it in its Clearing All of Memory Clearing all of memory erases all numbers, equations, and programs you've stored. It does not affect mode and format settings. (To clear settings as well as data, 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). 1­24 Getting Started 2 RPN: The Automatic Memory Stack This chapter explains how calculations take place in the automatic memory stack in RPN mode. You do not need to read and understand this material to use the calculator, but understanding the material will greatly enhance your use of the calculator, especially when programming. In part 2, "Programming", you will learn how the stack can help you to manipulate and organize data for programs. What the Stack Is Automatic storage of intermediate results is the reason that the HP 33s easily processes complex calculations, and does so without parentheses. The key to automatic storage is the automatic, RPN memory stack. HP's operating logic is based on an unambiguous, parentheses­free mathematical logic known as "Polish Notation," developed by the Polish logician Jan ukasiewicz (1878­1956). While conventional algebraic notation places the operators between the relevant numbers or variables, ukasiewicz's notation places them before the numbers or variables. For optimal efficiency of the stack, we have modified that notation to specify the operators after the numbers. Hence the term Reverse Polish Notation, or RPN. 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 and manipulate 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 2­1 T Z Y X 0.0000 0.0000 0.0000 0.0000 "Oldest" number Displayed Displayed The most "recent" number is in the X­register: this is the number you see in the second line of the display. In programming, the stack is used to perform calculations, to temporarily store intermediate results, to pass stored data (variables) among programs and subroutines, to accept input, and to deliver output. The X and Y­Registers are in the Display The X and Y­Registers are what you see except when a menu, a message, or a program line is being displayed. You might have noticed that several function names include an x or y. This is no coincidence: these letters refer to the X­ and Y­registers. For example, raises ten to the power of the number in the X­register. Clearing the X­Register Pressing { } always clears the X­register to zero; it is also used to program this instruction. The key, in contrast, is context­sensitive. It either clears or cancels the current display, depending on the situation: it acts like { } only when the X­register is displayed. also acts like { } when the X­register is displayed and digit entry is terminated (no cursor present). It cancels other displays: menus, labeled numbers, messages, equation entry, and program entry. 2­2 RPN: The Automatic Memory Stack Reviewing the Stack R (Roll Down) (roll down) key lets you review the entire contents of the stack by The "rolling" the contents downward, one register at a time. You can see each number when it enters the X­register. 2 3 4) Suppose the stack is filled with 1, 2, 3, 4. (press 1 Pressing four times rolls the numbers all the way around and back to where they started: T Z Y X 1 2 3 4 4 1 2 3 3 4 1 2 2 3 1 2 3 4 4 1 What was in the X­register rotates into the T­register, the contents of the T­register rotate into the Z­register, etc. Notice that only the contents of the registers are rolled -- the registers themselves maintain their positions, and only the X­ and Y­register's contents are displayed. R (Roll Up) except that it "rolls" the (roll up) key has a similar function to The stack contents upward, one register at a time. The contents of the X­register rotate into the Y­register; what was in the T­register rotates into the X­register, and so on. T Z Y X 1 2 3 4 2 3 4 1 3 4 1 2 4 1 2 3 1 2 3 4 RPN: The Automatic Memory Stack 2­3 Exchanging the X­ and Y­Registers in the Stack Another key that manipulates the stack contents is (x exchange y). This key swaps the contents of the X­ and Y­registers without affecting the rest of the stack. Pressing twice restores the original order of the X­ and Y­register contents. function is used primarily to swap the order of numbers in a calculation. The For example, one way to calculate 9 ÷ (13 × 8): 8 9 . Press 13 The keystrokes to calculate this expression from left­to­right 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 T­register (the top register) will be lost whenever a fifth number is entered. Arithmetic ­ How the Stack Does It The contents of the stack move up and down automatically as new numbers enter the X­register (lifting the stack) and as operators combine two numbers in the X­ and Y­registers to produce one new number in the X­register (dropping the stack). Suppose the stack is filled with the numbers 1, 2, 3, and 4. See how the stack drops and lifts its contents while calculating 1. The stack "drops" its contents. The T­(top) register replicates its contents. 2. The stack "lifts" its contents. The T­register's contents are lost. 2­4 RPN: The Automatic Memory Stack 3. The stack drops. Notice that when the stack lifts, it replaces the contents of the T­ (top) register with the contents of the Z­register, and that the former contents of the T­register are lost. You can see, therefore, that the stack's memory is limited to four numbers. Because of the automatic movements of the stack, you do not need to clear the X­register before doing a new calculation. Most functions prepare the stack to lift its contents when the next number enters the X­register. See appendix B for lists of functions that disable stack lift. How ENTER Works You know that separates two numbers keyed in one after the other. In terms 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 T Z Y X 1. 2 lost 3 4 5 5 2 3 1 2 3 4 1 2 3 4 5 3 4 5 6 4 3 3 4 11 Lifts the stack. 2. Lifts the stack and replicates the X­register. 3. Does not lift the stack. 4. Drops the stack and replicates the T­register. replicates the contents of the X­register into the Y­register. The next number you key in (or recall) writes over the copy of the first number left in the X­register. The effect is simply to separate two sequentially entered numbers. to clear the stack quickly: press 0 Y ou can use the replicating effect of . All stack registers now contain zero. Note, however, that you don't need to clear the stack before doing calculations. RPN: The Automatic Memory Stack 2­5 Using a Number Twice in a Row You can use the replicating feature of number to itself, press . Filling the stack with a constant together with the replicating effect of stack drop The replicating effect of (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 large would a population of 100 be at the end of 3 days? to other advantages. To add a Replicates T T 1.5 Z Y X 1 1.5 1.5 1.5 1.5 100 2 1.5 1.5 1.5 100 3 1.5 1.5 1.5 150 4 register 1.5 1.5 1.5 225 5 1.5 1.5 1.5 337.5 1. 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 Works Clearing the X­register puts a zero in the X­register. The next number you key in (or recall) writes over this zero. There are three ways to clear the contents of the X­register, that is, to clear x: 1. Press { } (Mainly used during program entry.) 2. Press 3. Press Note these exceptions: 2­6 RPN: The Automatic Memory Stack During program entry, deletes the currently­displayed program line and cancels program entry. During digit entry, backspaces over the displayed number. ), pressing If the display shows a labeled number (such as or cancels that display and shows the X­register. When viewing an equation, to allow for editing. During equation entry, function at a time. displays the cursor at the end the equation backspaces over the displayed equation, one For example, if you intended to enter 1 and 3 but mistakenly entered 1 and 2, this is what you should do to correct your error: T Z Y X 1 1 2 1 1 3 1 2 4 1 0 5 1 3 1.