CASIO fx-4500PA Section 1 Configuration and Operation Section 2 Manual Calculations Section 3 Integration Calculation Section 4 Program Calculation PROGRAM LIBRARY

The contents of this manual are subject to change without notice. No part of this manual may be reproduced in any form without the express written consent of the manufacturer.

The manufacturer assumes no responsibility for claims from third parties for loss or damages arising through the use of this calculator or manual.

The manufacturer assumes no responsibility for any loss or damages arising from loss of data and/or formulas incurred while using this calculator or manual. _,,

r Introduction Thank you for purchasing the Casio fx-4500PA. ~ This unit is an advanced programmable scientific calculator which features a 2-tier dis-~ play capable of displaying both formulas and results at the same time. The upper display

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features a 12-character dot matrix display capable of alphabetic and numeric display. The fx-4500PA also features a large-volume program memory, and is capable of per-forming integration calculations. A built-in formula memory is handy when performing repeat calculations, and manual calculations can be easily performed by following writ-ten formulas. Before using this unit, be sure to read these instructions thoroughly. When you're finished reading these instructions, be sure to keep this manual where you can refer to it often.

This manual is composed of four sections: 1. Configuration and Operation 2. Manual Calculations 3. Integration Calculation 4. Program Calculation

Section 1 should be read first to become familiar with the nomenclature, handling and cautions concerning this unit. Section 2, 3 and 4 can then be read in order to master these types of computations through samples and explanations.

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Section 1 Configuration and Operation ~~:a~~'.~.~~ .. :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Manual calculation modes ......................... 9

Di~~f ~;~~~;~:LL ) j~ Handling Precautions .............................................................................. 14

Replay function ............................................................................................. 48 Error position display function ....................................................................... 49 Multistatement function ................................................................................. 50

Scientific function calculations ........................................................... 52 Trigonometric functions and inverse trigonometric functions ......................... 52 Logarithmic and exponential functions .......................................................... 53 Performing hyperbolic and inverse hyperbolic functions ............................... 54 Coordinate transformation ............................................................................. 55 Permutation and combination ....................................................................... 56 Other functions (.../, x 2 , x- 1 , x!, V, Ran#) .................................................. 57 Fractions ....................................................................................................... 58

Power and Battery Replacement ......................................... 15 15 Replacing batteries .................................................

To replace the memory backup battery ........................................................ 15

:~t~e~~::r~~F;~~n:i~~~e~~ .. ....::.::.:.:.:.:..::.:.:.:.:.:::..:.:.:.::.:.::.::.:::::.:.::.:.:::.:.:.: ~~ Nomenclature and Functions ............................................................... 1s Before beginning calculations .... ........................................................ 27

Calculation priority sequence ................................... 27 Number of stacks ......................................................................................... 28 Number of input/output digits and calculation digits ..................................... 28

Overflow and errors ::::::::::::::::::::::::: ~~ ' Number of input characters ................................................ . ............................................................................................ ~ Corrections

Engineering symbol calculations ........................................................ 59 Binary, octal, decimal, hexadecimal calculations ........................ 60

Binary and octal block display ...................................................................... 61 Binary, octal, decimal, hexadecimal conversions .......................................... 63 Negative expressions .................................................................................... 64 Basic arithmetic operations using binary, octal, decimal and

hexadecimal values .................................................................................. 65 Logical operations ......................................................................................... 66

Statistical calculations ............................................................................ 67 Standard deviation ........................................................................................ 67 Regression calculation .................................................................................. 70

Formula memory function ..................................................................... 77 Purpose of the formula memory function ...................................................... 77

Section 2 Manual Calculations Ba::i~h~::i~~~~~~i~~s .................................................................................... ~:

35 ::~~:~~::~ ~;~~l~t~~~= .:::::::::::::::::::::::::::::::::::::::::::::::::::~::::_::_:::::::::::::;::::::: 36 Specifying the number of decimal places, the number of s1gnif1cant d1g1ts

37 and the exponent display ................................. 39 M~~g:~:~:~~~ i ~

. 44 (2) Independent memories ...........................

Section 3 Integration Calculation Input of function /(x) and integration calculation ........................ 84

Examples of operation .................................................................................. 85 Notes on integration calculation .................................................................... 88

Section 4 Program Calculation What is a program? .................................................................................. 90

Programming ................................................................................................ 90 Calculation formula ....................................................................................... 91 Registering filenames ................................................................................... 91 Writing programs .......................................................................................... 92 Program execution ........................................................................................ 93

Sp:n~:!rf~~~~~~~ .. :.::.:.:::.:.::..:::.::.:::::::::::.::::::::::.::::::.::::::::::::::::.::::::.::::::::: :: Omitting the multiplication sign ( x) .............................................................. 46 Continuous calculation function .................................................................... 47

Program correction, addition and deletion ..................................... 95 Inserting lines ............................................................................................... 95 Inserting a line at the beginning ................................................................... 95

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Editing programs .................................................. 95 Program deletion ........................................................................................ 100

Pr~i~~~:e~~:~~~:~ s~~~~h:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ~~~ Sequential search of program lines ............... ............................................. 103 Direct search ..................................... .... .. .... .. ................. 104 Scrolling right and left in filenames and program lines ............................... 106

Program execution ................................................................................. 107 Execution through filename search ............................................................. 107 Execution by pressing ~~ ..................................................................... 108 Aborting execution ...................................................................................... 109 Program debugging (correcting errors) ........................................................ 109

Convenient program commands ....................................................... 109 Jump commands ........................................................................................ 109 Subroutines ................................................................................................. 114 Pause command ......................................................................................... 117 Variable input command ............................................................................. 118 Fixm ............................................................................................................ 118

Remaining program capacity .............................................................. 120 Determining the number of remaining steps ............................................... 120

Using the unit as a data bank ............................................................ 121

PROGRAM LIBRARY 1. Prime factor analysis ........................................................................ 126 2. Greatest common measure ............................................................ 128 3 . .:i-Y transformation .......................................................................... 130 4. Minimum loss matching .................................................................. 132 5. Cantilever under concentrated load ........................................... 134 6. Normal distribution ............................................................................ 136 7. Numerical solution of an equation (Newton's law) ............... 138 8. Quadratic equation ............................................................................ 140 9. Complex numbers .............................................................................. 144 Error messages at-a-glance ................................................................ 154 Input ranges of functions .................................................................... 155 Specifications ........................................................................................... 158

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Section 1 Configuration and Operation

Key markings Modes

Display Handling Precautions

Power and Battery Replacement Nomenclature and Functions

Before beginning calculations ....

I Section 1 ))))) Configuration and Operation J Before using this unit for the first time, be sure to press the ALL RESET button on the back of the unit. Flow of Operations (Be sure to re.ad this!) In contrast to standard electronic calculators, the keys on "scientific" calculators often perform more thah one function. The following explains how to use these keys, so it's a good idea to read this section carefully before using your calculator for the first time.

I Key markings The fx-4500PA uses any given key to perform a number of different functions. For exam-ple, the key shown below is used to perform the following 5 functions: G): ( - ), 0: ;,;--, @: =,@:A,@: /A.

T' =

I< >I IA A

The function of this key differs depending on the operational mode the calculator is set to (see page 9), however if it is pressed directly, it performs the ( - ) function. If you press the @ill key and then press this key, it carries out the second function ;,;--. If you press the~ key and then press the [BJ key, it acts as the] key. And if you press it after pressing the@!!!] key, you can input the radical "A". Finally, you can use the [BJ key while in the BASE-N (see page 60) "HEX" mode to input the hexadecimal "/A". You'll notice that the key shows marks for each of these functions, which are color coded for easy identification. Referring back to the [BJ key, the function marked in orange is carried out after pressing the @ill key. After pressing the~ key, the [BJ key operates the function marked in light green. After pressing the @!!!] key, the function marked in red is carried out, and in the BASE-N mode, the [BJ key operates the function marked in green. Next, let's look at the bJ key. Note that the ''Ex2" mark is in blue brackets. The fx-4500PA 1z~d s . functions marked in these blue brackets are used for standard deviation (SD mode) and regression (LR mode) calculations.

Functions marked in ORANGE - Accessed by first pressing ~ key. Functions marked in LIGHT GREEN - Accessed by first pressing ~ key. Functions marked in RED - Accessed by first pressing @!!!] key. Functions marked in GREEN - Accessed in BASE-N mode. Functions marked by BLUE brackets - Accessed in SD mode or LR mode.

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r .[-M::--od-;--e-s ___________ II

the fx-4500PA it is necessary to select the proper mode to suit your calcula-When us1_ng t This ca~ be done by using the~ key in combination with the num-tion requ1remen s. . . ber keys. (Refer to plate below the display window.)

Manual calculation modes Calculation modes

@(]]: COMP mode . . General calculations, including function calculations.

(@[}]: BASE-N mode . I I _ . t I decimal hexadecimal conversion and calculations, as well as og1ca oper Binary, oc a , '

ations.

@m: LR mode . . h th d I lation ("LR" symbol appears in display window w en 1s mo e 1s Regression ca cu

selected.) @I]]: SD mode . h th" d Standard deviation calculation. ("SD" symbol appears in display window w en 1s mo e is selected.) *Modes[]]- rn are totally independent, and cannot be used together.

@8: Eng mode . h th" d Engineering symbol calculation. ("Eng" symbol appears in display window w en 1s mo e is selected.) (Refer to page 59.) *The calculation mode last selected is retained in memory when the fx-4500PA's power is switched OFF.

Angular measurement modes @[!): Deg mode . . d h

"d ees" (" I!] " symbol appears in display win ow w en Spec1f1es measurement in egr . this mode is selected.)

~rn: Rad mode . h th. t " d" ns" (" liJ" symbol appears in display window w en is Spec1f1es measuremen in ra 1a .

mode is selected.) ~[[]: Gra mode . . h th"

" ds" ("""" symbol appears m display window w en is Specifies measurement in gra . ~ mode is selected.)

d d '4' [[] can be used in combination *With the exception of the BASE-N mo e, mo es '-"-' -with the manual calculation modes.

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Display modes @@rn: Fix mode Specifies number of decimal places. ("Fix" symbol appears in display window when this mode is selected.) ~(]): Sci mode Specifies number of significant digits. ("Sci" symbol appears in display window when this mode is selected.) ~(]): Norm mode Cancels "Fix" and "Sci" specifications. This operation also changes the range of the exponent display (see page 12). *With the exception of the BASE-N mode, modes [l) - 00 can be used in combination with the manual calculation modes.

The mode last selected is retained in memory when the fx-4500PA's power is switched OFF. Program calculation mode ~@): WAT mode S~ecified when ~riling or ~orrecting programs (files). ("WAT" symbol appears in display window when this mode 1s selected.) Press again to cancel WAT mode. ~~: Defm mode _Press to expand number of memories. ("Defm" appears in display window when this mode 1s selected.) After specifying this mode, input a value and press the @) key to specify the number of useable memories (see page 41.)

I Example I ~ ~ 10 @J - Number of memories expanded by 10. Mode Hierarchy Diagram

MANUAL CALCULATIONS

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WAT

Abbreviations COMP Compute Dec Decimal number

LR Linear regression Hex Hexadecimal number SD Standard deviation Bin Binary number

Eng Engineering Oct Octal number To return to standard operation (initialized state) press~ I]] (COMP mode) - ~ [!) (Deg mode) - ~ 00 (Norm mode)

r Display Two-tier display This unit features a two-tier display. The upper tier is a dot display which features an input buffer, for display of up to 12 characters. The lower display is capable of displaying 10 digits for a mantissa, as well as 2 digits for an exponent. When formulas are input, they are displayed on the upper display, and then results are shown on the lower display when the @) is pressed to execute the calculation. This allows both the formula and the result to be displayed simultaneously. In addition, when filenames are displayed, the file name is shown on the upper display, with the file number shown on the lower display. When programs are displayed, the pro-gram data is displayed on the upper display, with the program line number shown on the lower display.

I Example I 2 x 3 = 6

I Example I Filename

I Example I Program

I! 6. l!IT Formula Result of calculation

PROGRAM

9 I File number Filename

File number Program line number Program data

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Display symbols The display window features symbols which light to indicate the present operational sta-tus of the fx-4500PA.

ill: [[]: [Ml: [!]: hyp: WRT: ffi: @IT]: mm: LR: SD: l!l: rn: [!): Fix: Sci: Eng:

ff!!! !!!!! !!!!! !!!!! !!!!! !ii!! !ii!! !!!!! !!!!! !!!!! !!!!! !!!!! .. ilii ""' 1111 !!!!i iiiil 1111 iiiii fill !liii 11111 iii!I !l!li .. n n ,, ,, ,, ,, ,, ,, n ,,_pp

c1.c1.c1.c1.c1.c1.c1.c1.c1.a. -u @ (fl !Ml @ hyp WRT (Tiill (@) B'l!I LRSD [!] llml Fix Sci Eng

Indicates @!ill key has been pressed. Indicates lfilB key has been pressed.

Indicates~ key has been pressed. Indicates @!00 key has been pressed. Indicates ~ key has been pressed. Indicates calculator in the WRT mode. Indicates filename or program (file contents) is displayed. Indicates program is being edited in WRT mode. Indicates intermediate result is displayed. Indicates LR mode has been specified. Indicates SD mode has been specified. Indicates angular measurement in units of "Degrees". Indicates angular measurement in units of "Radians". Indicates angular measurement in units of "Grads". Indicates specification of number of decimal places is being executed. Indicates specification of number of significant digits is being executed. Indicates Eng mode has been specified.

+- -+: Indicates number of characters exceeds limitation of screen. Non-displayed characters can be viewed by "scrolling" right or left, as indicated by arrow(s).

Exponential display During normal calculation, this unit is capable of displaying up to 1 O digits. However if calculation results exceed this limit, they are automatically displayed in exponential for-mat. You can choose from two different types of exponential display formats:

(A) 10-2(0.01)> lxl, lxl ~10'0 : Norm 1 mode (B) 10-9(0.000000001)> Ix I , Ix I ~ 1010 : Norm 2 mode

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r ! . f these modes can be carried out by pressing ~[[). when no specification selection o 'f' t d' 't been made for the number of decimal places or s1gm 1can 1g1 s. .

has t t t s is not displayed so it is necessary to perform the following procedure The presen s a u to specify either display format:

Hr~2oor@ ~1 1/200 ~ -031 (Format A) ~1 1/200 I (Format B) 0.005

Ill

The examples given in this manual shows calculation results in exponential display for-

mat "A".

How to view the calculation results in exponential format.

1.2E11

L__J LJ Mantissa Exponent

-+ 1.2x 1011 .. 120,000,000,000

1.2E-3 1.2-03

Ill L__J LJ

Mantissa Exponent

.. 1.2x 10- 3 -+ 0.0012

Special display functions . For fractional, hexadecimal and other special calculations, results are shown on the dis-play as follows: Fractions

456..112..123 456..112..1 23.

Ill L..........J L---J L---J Integer Numerator Denominator

12 (Indicates 456 231

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Hexadecimal numbers

ABCDEF12 AbCdEF12 H [Indicates ABCDEF1216 ( = -141256727810)]

Sexagesimal numbers

12.58244 12a 34a 56.78 [Indicates 1234'56. 78"] L.._J L_J [____J

Degrees Minutes Seconds

I Handling Precautions This unit is composed of precision electronic components, and should never be disas-sembled. Do not drop it or otherwise subject it to sudden impacts, or sudden changes in temperature. Be especially careful to avoid storing the unit or leaving it in areas ex-posed to high temperature, humidity or large amounts of dust. When exposed to low temperatures, the unit will require more time to display answers and may even fail to operate. The display will return to normal once normal temperature is attained.

The display will appear blank while the unit is performing calculations. At this time most keys will be inoperative. Because of this, keys should normally be used while confirm-ing proper operation by checking the display.

Batteries should be replaced every 5 years, even if the unit is not used for extended periods. Never leave dead batteries in the battery compartment. They can leak and damage the unit.

Avoid using volatile liquids such as thinner or benzine to clean the unit. Wipe it with a soft, dry cloth or a cloth that has been dipped in a neutral detergent solution and wrung out.

Note that the manufacturer assumes no responsibility for any loss or claims by third parties which may arise from use of this product.

Note that the manufacturer assumes no responsibility for any damage incurred as a result of data loss caused by malfunction, repairs or battery replacement. The user should prepare physical records of important data to protect against such data losses.

If this unit should malfunction, be sure to contact your nearest Casio dealer or service center, explaining the problem in detail.

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llQ_P_o_w_e_r_an~d:tnB~at~te~r~ytR~e~p~la~c~emm~errntt""""~~~~l\11 . su lied to this unit by one CR2032 lithium battery, which is used for normal

Power is PP II one CR2032 lithium battery used for memory backup. operations, as we as removed at the same time, programs and data will be lost, If both of these batteries are .

'd eplacing them at the same time. so avo1 r . have been removed from the unit for some reason, replace them *If both batteries ON and press the "All Reset" button after turning the power

Replacing batteries . . . k the "Low Battery" indicator appears on the display. If batteries become wea I _Low battery ntinue to use the unit after this display appears, power will turn OFF automati-

lf you C(l 0 eration will become impossible even if you press the flm ON key. If th IS O?-cally andl p th CR2032 battery as soon as possible. Do not leave dead batteries in curs rep ace e the ~nit. Doing so may result in damage or lost memory contents.

To replace the memory backup battery The battery used for memory backup should be replaced every two years. G)Press the I@ key. Then remove the two All Reset button

screws on the back of the unit and remove the back cover.

@Remove the screw holding the battery pres-sure plate (screw "B") and then remove the battery pressure plate.

@Remove the old battery from th~ unit. . (This can be done easily by turning the unit so that the battery compartment is facing downwards, and then lightly tapping the unit.)

@Wipe the surfaces.of the new battery with_a soft dry cloth and load them into the unit, making sure that the positive (B side is fac-ing upwards.

@Fasten the battery pressure plate in place us-ing the screw.

@Replace the back cover and press the @ key. Memory contents are protected by the main battery in this case.

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Screw

Screw "B"

To replace the main battery /All Reset button CD Press the l!fl key. Then remove the two

screws on the back of the unit and remove the back cover.

@Remove the screw holding the battery pres-sure plate (screw "A") and then remove the battery pressure plate.

~7 )screw

@Remove the old main battery from the unit. (This can be done easily by turning the unit so that the battery compartment is facing downwards, and then lightly tapping the unit.)

Wipe the surfaces of the new battery with a soft, dry cloth and load them into the unit, making sure that the positive ffi side is fac-ing upwards.

Fasten the battery pressure plate in place us-ing the screw. Then press the@] key.

Replace the back cover. Memory contents are protected by the memory backup battery in this case.

~ /_Screw "A"

Avoid changing both batteries at the same time as doing so may result in memory contents being lost.

Precautions: Incorrectly using batteries can cause them to burst or leak, possibly damaging the interi-or of the unit. Note the following precautions:

Be sure that the positive ffi and negative 8 ~:~i'!~:~~-poles of the battery are facing in the proper ~~ direction.

Never leave a dead battery in the battery compartment. Remove the battery if you do not plan to use the unit for long periods. Replace the battery at least once every 5 years, no matter how much the unit is used during that period.

Never try to recharge the battery supplied with the unit.

Do not expose batteries to direct heat, let them become shorted, or try to take them apart.

Keep batteries out of the reach of small children. If swallowed, consult with a physi-cian immediately.

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Auto Power-OFF function . battery life this unit will turn OFF automatically if it is not used for approx1-To preserve . t t e

I 6 minutes To restore power, press the ma key. Note that memory con ens ar matey protected even when power goes OFF.

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I Nomenclature and Functions

Second shift key

Function command keys

Numeric keys Other command keys

Exponent key

l!ffiill Shift key

1 Display window

Cursor keys Power OFF key

Mode key

Arithmetic operation keys

Execute key

Press whe.~ u~in~ the function com_mands and functions marked in orange on the key ~anel. An ~ ~111 appear on the display to indicate that llE!ill has been pressed. Press-ing llEiill again will cause the "(!]" to disappear from the display and the unit to return to the status it was in before llE!ill was originally pressed.

~ Second shift key Press when u~in~. th_e function comm~nds and functions marked in light green on the ~ey panel. ~n ~ will appear on the display to indicate that~ has been pressed. Press-ing~ again will cause the "[]" to disappear from the display and the unit to return to the status it was in before~ was originally pressed.

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@ Mode key Press when setting the status of the unit or when specifying the unit of angular measure-ment. Refer to page 9 for details on modes.

~K Alphabet key Press to input alphabetic characters or special characters. Pressing~ displays "[!]" and allows the input of only one character. After the character is input, the unit returns to the status it was in before the l@!l key was originally pressed. Pressing llE!ill followed

by~will lock the unit in this mode and allow consecutive input of alphabetic characters until~ is pressed again.

0 0 0 0 0 0 0 0 0 0 0 0 (!!] 0 0 0 CD [I)

0 !ID () [[) m [IJ 0 0 @] !El m QJ

IBJ m 00 DD (ID @] [E] @] I]] rn [!J [[] [fl ~ 00 !YI [LI ~ D

Rnd 1-ni Ran# @) - LJL , 8 Numeric keys LXJ X Ljq.t

ILJ IIJ !ID LYJ LyQiiJ

'"""' (!) !ID (ID ,.,,,, ,,,, ,...,, III II) [!) LR mode (~00)

L2%1J Lz.J LnJ

[[) [!] LX'.J Lzo;,J

ill !ID 00 Used in combination with ~ key.

(!) !ID (I] III II) [!)

lz.rJ LzxJ LnJ

SD mode (~[j])

[ID 8 L,X'.J lxq,,J

Whe~ the l!Hi!il key is pressed in the COMP mode, LR mode or SD mode the following functions are specified: '

l!illl [ID ............. Internal rounding This key operation rounds the internal value (value stored in the y register) to 1 O digits. Note that this also rounds the result that is pr_oduced by the Ans function. In the FIX and SCI modes, this key oper-

.... at1on changes the internal value to the form specified for value display. l!illl ~- ........... Random number generation

Generates random numbers between 0.000 and 0.999.

For information on other functions, see "Engineering symbol calculations" on page 59.

The following functions can be specified by pressing 1!!iJ in the LR mode or SD mod (only some functions are available). e

~Cf! ........... x (Mean of x) ~~ ........... Ex2 (Sum of squares of x) liiil l:!l . . . .. . . . . . . Ex (Sum of x) ~CJJ ........... n (Number of data) ~~ .......... Ey2 (Sum of squares of y) l!il~ ........... Ey (Sum of y) ii)~ ........... Exy (Sum of products of x and y) li!il CfJ ........... y (Mean of y) ~C!J ..... : ..... yu. (Standard deviation of y) ~c;!l yun-1 (Sample standard deviation of y) ~ ~ . . . . . . . . . .. xu. (Standard deviation of x)

These f~nctions are used in standard deviation and regression calculations. For details see sections on "Standard deviation" (page 67) and "Regression calculation" (page ?O)'.

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1filJ Exponent/Pi/Standard deviation calculation key lXO'lt

CAPA

~ Answer/CAPA/Space key SPACE

Press ~ followed by@) to recall the last calculation re~u.lt. . Hold down following @ key to display number of remarnrng steps rn program. Press following @@ key to input a space.

INS rnru Delete/Insert key Press@] to delete character where curs.or is flashing. Deletes character to left of cursor

hen cursor is to the right of the last rnput character. wp following@ key to display the insert cursor (: : ). Entering a value while the in-ress .h ... sert cursor is displayed inserts the value rn t e posrtron rmmediately preceding the in-sert cursor location.

Mel

miJoN All clear/Memory clear/Statistical data clear/Power On key LScl.J

Press to clear all input characters or formulas. Also, press to clear Error Check mes-sage on display.

Pressing @ followed by ma clears all data in unit's memory. Pressing~ followed by ma clears contents of statistical calculation memory. Press when power is OFF to turn power ON.

Goto Lbl

~T~ Cursor/Replay/Jump command keys REPLAY

Press to move the cursor to the left or right on the display to correct formulas or numer-ic values.

Pressing~ moves the cursor to the left, while pressing ~ moves it to the right. Press-ing either key and holding it down will cause continuous movement of the cursor in the respective direction.

Once a formula or numeric value is input and@) is pressed, these keys become replay keys. Pressing ~ displays the formula or numeric value from the end, and pressing ~ displays it from the beginning. Pressing @) again will re-execute (see page 48).

These keys are also used to input "Jump" commands which alter program execution. Pressing~ followed by~ enters the "Goto" command. Pressing~ followed by~ enters the "Lbl" (Label) command. For details, refer to page 109.

@ff) Power OFF key Press to turn the unit's power OFF. Note that mode setting and memory contents are protected even when power is turned OFF.

lfilID File key Press to recall registered files. For details, refer to page 96. IN

@!) Formula memory key Used when making calculations using registered formulas. For details, refer to page 77.

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[illID Formula memory I Program I Multistatement key. = to execute formulas in formula memory. For detarls, refer to page 77. Press~ f 108

S 'SiifFil followed by @ill] and @) to execute programs. For detarls, re er to page . Pres E"-" d I I

=followed by @ill] to separate formulas or commands rn programme ca cu a- Press~ . . . k " 1

r Consecutive calculations The result of such combrnatrons rs nown as a mu -tiOOSO . tistatement". For details, refer to page 50.

1@ File line scroll up/Integration/Display key . . . Press while file contents are displayed to scroll up to the prevrous fr le lrne . Press @ followed by [QI when making integrations. For details, refer to page 84. Press @fl followed by [QI to display results of program calculations and consecutrve cal-culations.

A'"" File line scroll down/ Absolute value/Pause command/ [Q) SEARCH Search key Press while file contents are displayed to scroll down to the next file line. Press@ followed by [QJ when making absolute value calculations.

Press~ followed by [QJ to input "Pause" command . .For details, refer to page 117. Press to search contents of file using "Search" function. For details, refer to page 105.

~ Engineering/Judge command/Not key Not " Each press of this key shifts the decimal of the displayed value three decrmal places to the right or left. This in effect results in conversion of the value from one metrrc unrt to another, such as 10-3 milliseconds, 10-5 microseconds, 10 12 picoseconds, or 103 kilohertz, 106 megahertz, 109 gigahertz.

I Example I 12.3456@1 1st time~ is entered 2nd time ~ is entered 3rd time ~ is entered 4th time ~ is entered

12.3456@) 1st time@~ is entered 2nd time @~ is entered 3rd time @~ is entered

12.3456 12.3456 00 12345.6 -o3

12345600. - 0"._ 12345600. - 06 (No change)

12.3456 0.0123456 03

0.000012345 06 0.000000012 09

-

0.000000012 09 4th time @~ is entered (No change) When pressed after pressing~ key, "judge" symbol"=>", used in executing Jump

command, is input. For details, refer to page 112. When pressed in BASE-N mode, this key executes "Not" function used in logical operation.

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die :::\:>

~ Fractions/Judge command/Negative key Used when inputting fractions and mixed numbers.

I Example I To input 23 , press 23@@IJ45: To input 2~, press 2@I)3@IJ4: 45 4

By pressing@~ in succession, the displayed value will be converted to the improper fraction.

When pressed after pressing M key, "judge" symbol " ", used in executing Jump command, is input. For details, refer to page 112.

Press in the BASE-N mode prior to entering a value to obtain the negative of that value. The negative number is the two's complement of the value entered.

X' ~

la Square root/Square/Judge command/Decimal value key DecLdJ

Press prior to entering a numeric value to obtain the square root of that value. Enter a value, and press this key following @ to obtain the square of the value. When pressed after pressing M key, the "judge" symbol "t.. ", used in executing Jump command, is input. For details, refer to page 112.

Press in the BASE-N mode to specify the decimal calculation mode. When pressed following @ in the BASE-N mode, the subsequently entered value is specified as a decimal value.

'~m Common logarithm/Exponent of 10/Variable fix command/ Hex'h' Hexadecimal key Press prior to entering a value to obtain the common logarithm of that value. When pressed following the@ key, the subsequently entered value becomes an ex-

ponent of 10. When pressed following the M key, "Fixm" is entered. For details, refer to page 118. Press in the BASE-N mode to specify the hexadecimal calculation mode. When pressed following @ in the BASE-N mode, the subsequently entered value is specified as a hexadecimal value.

e" { Uill Natural logarithm/Exponential/Variable input command/Binary key BlnLbJI

Press prior to entering a value to obtain the natural logarithm of that value. When pressed following the@ key, the subsequently entered value becomes an ex-ponent of "e".

When pressed following the M key, the " [ " symbol used in executing the variable input command is input. For details, refer to page 118.

Press in the BASE-N mode to specify the binary calculation mode. When pressed following the @ key in the BASE-N mode, the subsequently entered value is specified as a binary value.

-24-

'@ power/Root/Variable input command/Octal key 001

'0

'1 press this key and then enter y (any number) to calculate x to the power of y.

Enter x, . = T alculate the xth root of y, press after pressing ~.

0 c essed following the M key the " l " symbol used in executing the variable

When pr ' . ut command is input. For details, refer to page 118. inp 1n the BASE-N mode to specify the octal calculation mode .

press . When pressed following the @ key in the BASE-N mode, the subsequently entered value is specified as an octal value.

'fgj Negative/Cube root/Equal key ~ A I f Press prior to entering a numeric value to make that va ue nega 1ve.

[xampl~ -123-+ [8123 . Press following the@ key to obtain the cube root of a subsequently entered numeric value.

Press following the M key to enter the "=" sign.

.. "' B Decimal - Sexagesimal/Not equal key 18 s Press to enter sexagesimal value. (degree/minute/second or hour/minute/second)

[xample] 7845'12"-+ 788458128 When pressed following the @ key, a decimal based value can be displayed in degrees/minutes/seconds.

Press following the M key to input the """" sign.

~ Hyperbolic/Relational operator key c c f Pressing~ and then~.) or(@ prior to entering a value produces the respec 1ve hyperbolic function (sinh, cosh, tanh) for the value.

Pressing@, then~ and then~.) or(@ prior to entering a value produces the respec-tive inverse hyperbolic function (sinh- 1 , cosh-1, tanh- 1) for the value.

Press following the M key to enter the """" sign.

sin' :s , .... > tan'< Trigonometric function/Inverse trigonometric function/ ~ I] ~ v o 1 e F Relational operator keys Press one of these keys prior to entering a value to obtain the respective trigonometric function for the value.

Press@ and then one of these keys prior to entering a value to obtain the respective inverse trigonometric function for the value.

PressM and then one of these keys to input the"~",">" and"

Int lfilID Store memory/Integer/Constant term key LAJ it Press prior to inputting alphabet character when inputting calculation results to memory. Press ~ key followed by~ key prior to inputting number in order to obtain integer part of that number.

Press following~ key in LR mode to calculate constant term "A" in regression formula. (gill]~ ............ Calculation of A (Constant term of regression formula)

Frac

IBID;] Recall memory/Fraction/Regression coefficient key LBJ

Press prior to inputting alphabet characters to display value input into memory. Press~ key followed by@) key prior to inputting number in order to obtain fraction part of that number.

Press following~ key in LR mode to calculate regression coefficient "B" in regres-sion formula.

(gill]~ ............ Calculation of B (Regression coefficient of regression formula)

x[I]- "'m Parentheses/ Reciprocal I Factorial/ Correlation coefficient/ ( ) crJ a L:l!J H Estimated value of x key Press the open parenthesis key and the closed parenthesis key at the position required in a formula. Press~ followed by [I) prior to entering a value to obtain the reciprocal of that value. Press~ followed by OJ after entering a value to obtain the factorial of that value. In the LR mode, press following the~ key for coefficient of correlation calculation and estimated value of x in linear regression calculation, respectively.

(gill] c::p ............ Calculation of r (correlation coefficient) (gill]Cfl ............ Calculation of x (estimate of value of x)

,~ Comma/Semicolon/Estimated value of y key Press to enter comma in statistical and other formulas. Press following~ to enter semicolon. In the LR mode, press following the~ key for the estimated value of y in regression calculation. M-(M.J Memory plus/Memory minus/Data input/Clear key

LDTJLCLJJ

Press to add displayed value to memory. Note that when formula is displayed, results are first derived and then stored into memory.

Press following~ key to subtract displayed value from memory. In the LR and SD modes, press to input data. In the LR and SD modes, press following the~ key to clear data which has been input incorrectly.

-26-

[Before beginning calculations.... I Calculation priority sequence . . This unit employs true algebraic logic to calculate the parts of a formula 1n the following order: (i)Coordinate transformation/integration Pol (x, y), Rec (r, II), fdx @Type A functions . .

These functions are those in which the value is entered and then the function key 1s pressed. x2. x ', x!, 0 ' ", Eng symbols

@Power/root xY, v-@Fractions able @Abbreviated multiplication format in front of 7r, memory or parenthesis 27r, 5A, 7rR, etc. @Type B functions .

These functions are those in which the function key is pressed and then the value 1s entered. v , V , log, In, e-', 1 O', sin, cos, tan, sin , , cos 1 , tan 1 , sinh, cosh, tanh, sinh 1 , cosh 1 , tanh 1 , Int, Frac, Abs, ( - ), (following in BASE-N mode only) d, H, b, o, Neg, Not

(?)Abbreviated multiplication format in front of Type B functions 2../3, A log2, etc. @Permutation, combination nPr, nCr @x, _,_ @+, -@and ] In BASE-N mode only. @or, xor, xnor

*When functions with the same priority are used in series, execution is performed from right to left for: ex1n..J120 --+ e'\ln(..J120)l

Otherwise, execution is from left to right.

*Everything contained within parentheses receives highest priority.

I Example I 2 + 3 x (log sin27r2 + 6.8)-22.07101691 (in the "Rad" mode) w

LJu L_L_J

'2.J

-27-

Number of stacks This u~it features a memory known as _a "stack" for the temporary storage of low priority

numen~ values and commands (functions, etc.). The numeric value stack has nine lev. els, while the command stack has 24. If a complex formula is employed that exceed the stack space available, a stack error (Stk ERROR) message will appear on the display~ I Example I 2 x ( ( 3 + 4 x ( 5 + 4 ) + 3) + s) + a =

~lll~l~ll4l~ Numeric stack value Command stack

CD 2 rn x @ 3 ~ ( 4 ~ ( 5 @] + 4 [ID x

[] ( ITl +

*Calculations are performed in the order of the highest calculation priority first. Once a calculation is executed, it is cleared from the stack.

Number.of input/output digits and calculation digits The allowable input/output range (number of digits) of this unit is 1 o digits for a mantis-sa, and 2 digits for an exponent. Calculations, however, are performed internally with a range of 12 digits for a mantissa and 2 digits for an exponent.

I Example I 3x105+ 7=

3~5~71:142857~

3E5/7 42857 .14286

Ii]

3E5/7 - 42857 0.1428571

Ii]

Once a calculation is completed, the mantissa is rounded off to 10 digits and displayed. I Example I 3x105+ 7=

3E5/7 42857 .14286

Ii]

-28-

1:142857~

overflow and errors

42857 .14286 - ~ 0.14286

Ii]

If the operational range of the unit is exceeded, or incorrect inputs are made, an error message will appear on the display and subsequent operation will be impossible. This is carried out by the error check function. The following operations will result in errors: (1) The answer, whether intermediate or final, or any value in memory exceeds the value

of 9. 999999999 x 1099 (2) An attempt is made to perform function calculations that exceed the input range. (See

page 155.) (3) Improper operation during statistical calculations. (Ex. Attempting to obtain x or xan

without data input.) (4) Illegal argument.

(Ex. Negative value specified for Defm) (5) The capacity of the numeric value stack or the command stack is exceeded.

(Ex. Entering 23 successive IIJ's followed by 20314) (6) Input errors are made. (Ex. 5tt3 (7) Even though memory has not been expanded, a memory such as Z (2] is used. (See

page 42 for details on memory.) (8) When Prog command (see page 114) causes subroutine nesting overflow. (9) When no Lbl corresponds to Goto command (see page 1.11), or when no filename

corresponds to Prog command (see page 114). When error messages appear, most keys will become inoperative. In this case, press the a!J key to return to normal operation. You can also press the @5 key or~ key, caus-ing the cursor to show the position of the error (see "Error position display function" on page 49).

The following error messages will be displayed for the operations noted above: (1)-(3) Ma ERROR (4) Arg ERROR (5) Stk ERROR (6) Syn ERROR (7) Mem ERROR (8) Ne ERROR (9) Go ERROR

Ne ERROR and Go ERROR messages mainly occur when using programs. (Refer to the Error Message Table on page 154.)

-29-

Number of input characters ~ """"~'" '"'ra"" "" beoo '"''"d"' io ' IO

Section 2 Manual Calculations

Basic calculations Memory

Special functions Scientific function calculations

Engineering symbol calculations Binary, octal, decimal, hexadecimal calculations

Statistical calculations Formula memory function

I Section 2 ))))) Manual Calculations I Basic calculations Arithmetic operations Arithmetic operations are performed by pressing the keys in the same order as noted

in the formula. For negative values, press !BJ before entering the value.

Example

23+4.5-53= -25.5

56x (-12)+ (-2.5) = 268.8

12369 x 7532 x 74103 = 6.903680613x 10 12 (6903680613000)

(4.5x 1075 ) x (-2.3x 10-79 ) = -1.035x10- 3 ( - 0.001035)

(2+3)x 102 =500

Operation

2304.51:153@]

1236913753213 74103@]

4.5@]75131B]2.3@]1BJ 79@]

ITJ203CDl31@12@1 *The correct answer cannot be derived by entering CD203CiJ@l2. Be sure to enter t3 1 between the rn and @I in the above example.

(1x10 5)+ 7= 14285.71429

(1 x 105 ) + 7-14285 =0.7142857 1@]5PJi71:114285@]

*Internal calculations are calculated in 12 digits for a mantissa, and the result is displayed rounded off to 1 O digits. Internally, however, the mantissa is calculated to 12 digits.

-34-

Display (Lower) -25.5

268.8

6.903680613 12 I

-1.035-03

500.

14285. 71429

0.7142857

For mixed basic arithmetic operations, multiplication and division are given priority over addition and subtraction.

Example Operation Display (Lower) -

3 +5x6=33 305136@1

7x8-4X5=36

Parenthesis calculations Example Operation

100 - (2 + 3) x 4 = 80 1 OOl:IITJ203CDl34@1

2+3 x (4+ 5) = 29 20313ITJ405@1 *Closed parentheses occurring immediately before operation of the 11!!1 key may be omitted, no matter how many are required.

~-~X~+~=~ I ITJ71:12CDITJ805@1 A multiplication sign t3 occurring immediately before an open parenthesis can be omitted.

10-(2+7x(3+6)]= -55 I 101:1ITJ207ITJ306@1 *Henceforth, abbreviated style will not be used in this manual.

2 x 3 + 4 =(2x 3+4)+5=2 5 5x6+6x8 0_8125

15x4+12x3

(1.2x1019)- ((2.5x10 20 ) xi_]=4.5x1018

100

6 4x5 =0.3

ITJ513606138CDP1i ITJ15134012133CD@l

1.2@]191:1ITJ2.5@1 20133P1i100CD@J

*The above is the same as ~11!.i1411!.i151!!!J.

-35-

33.

36.

6.6

Display (Lower) 80.

29.

65.

-55.

2.

0.8125

4.5 18

0.3

Percentage calculations Premium and discount calculations cannot be performed in the Eng Mode. To perforrn a premium or discount calculation, first press ~8 to exit the Eng Mode. See page 59 for details.

Example

Percentage 26% of $15.00

Premium 15% increase from $36.20

Discount 4% discount from $47.50

Ratio 75 is what % of 250?

Rate of change 141 is an increase of what % from 120?

240 is a decrease of what % from 300?

Operation Display (Lower)

15t261lE!ill~ 3.9

36.2t151lE!ill~O 41.63

47.5t41lE!ill~l:I 45.6

75~2501lE!ill~ 30. (%)

1411:11201lE!ill~ 17.5 (%)

2401:13001lE!ill~ - 20. (%)

-36-

Specifying the number of decimal places, the number of significant digits and the exponent display

TO specify the number of decimal places (Fix), press ~followed by!]], and then a value indicating the number of places (0-9). (The "Fix" indicator will appear on the display.)

TO specify the number of significant digits (Sci), press~ followed by!~], and then a value indicating the number of significant digits (0- 9 to set from 1 to 10 digits with "O" indicating 10 digits). (The "Sci" indicator will appear on the display.)

Pressing the~ key or llE!ill followed by liW will cause the exponent display for the num-ber being displayed to change in multiples of 3.

The specified number of decimal places or number of significant digits will not be can-celled until another value or ~[ID is specified. (Specified values are not cancelled even if power is switched OFF or another mode (besides ~[ID) is specified.)

100 cancels Fix and Sci specifications, however the range of the exponent display can be set. Each time ~[ID is input, operation switches between Norm1 and Norm2.

Norm 1 : All values less than 102 or greater than 109 are automatically expressed as exponents.

Norm 2 : All values less than 10-9 or greater than 109 are automatically expressed as exponents.

Even if the number of decimal places and number of significant digits are specified, internal calculations are performed in 12 digits for a mantissa, and the displayed value is stored in 10 digits. To convert these to the specified number of decimal places and significant digits, press llE!ill followed by ~-

This operation is invalid in the BASE-N mode. To make this specification in the BASE-N mode, first press ~ followed by [[).

Example Operation

100"'" 6=16.66666666 ... 100~6~ (Four decimal places specified.) ~!]][!)

I (Specification cancelled.) ~[ID .,~ r::::::::::,:.~::

*Values are displayed rounded off to the place specified. I (lith Norm1specified.)1~1000~ I (Norm2 specified) ~[ID

-37-

Display (Lower) 16.66666667

16.6667 Fix

16.66666667 1.6667 1

Sci

16.66666667

1. -03

0.001

200+ 7x 14=400 200~7t141ili) (Three decimal places specified.) ~ID!]]

I (Calculation continues with 10 digits.) 200~71ili)

141ili)

If the same calcu ration is performed with the specified number of digits:

200~71ili)

(Value stored internally cut off at specified decimal place.) @~

123m x 456 = 56088m

=56.088km

78g x 0.96 = 74.88g =0.07488kg

141ili) (Specification cancelled.)~[[)

-38-

123t4561ili)

78t0.961ili) @lill]

(Upper)

400, 400.000

Fix

28.571 Fix

.. 8.57142857 x F~

400.00Q Fix

28.571 Fix

28.571 Fix

(Upper) 28.571 x Fix

399.994 Fix

399.994

56088. 56.088 03

74.88 0.07488 03

.Qv1emory This unit contains 26 standard memories. There are two basic types of memories, the memories, which are accessed by using the lillJ and!@ keys in combination with the 26 letters of the alphabet, and the memories, which are ac-cessed by using the~,@@:], (@and@ keys. The variable memory and independent memory utilize the same memory area. contents of both of the variable and independent memories are protected even when the power is turned OFF.

(1) Variable memories Up to 26 values can be retained in memory at the same time, and can be recalled when desired. @!

. ~OO B- 5608~ If a variable expression 1s entered, the expression is first calculated ac d. t h t d . th . bl cor ing o t e values

s o'.e in e varia e memories used in the expression. The result is then st variable memory specified for the result. ored in the

I Example I Inputting the results of Ax B into memory "C":

,____/ Ax B_J I c ~ 6898824.J ..___I _J

c ~ 6898824. ] Sy~ ~RROR is generated when an attempt is made to input a substitution formula (such as -Ax B) or multistatements (such as Ax B : c x D) and the e t" tents are retained. ' xis ing memory con-

When input is made in a format such as "S = log2" where the bl f 1 varia e 1s equal to the ormu a, the results of the calculation are input into the specified memory.

J Example J Executing "S = log2":

-40-

S=log 2_

S=log 2 0.301029995

J

S= 0.301029995

*In the SD mod~, variable memories S,T and U are used as statistical memories. In the LR mode, variable memories N, 0, P, S, T, and U are used as statistical memories. In addition, G, H, I, J, K, L, and X can be used as integral memories. These variable memories cannot be used simultaneously while making statistical or integral calculations.

Array-type memories Up to this point, all of the memories used have been referred to by single alphabetic charac-ters such as A, B, X, or Y. With the array-type memory introduced here, a memory name (one alphabetic character from A through Z) is appended with a subscript such as [1] or [2]. *Brackets input by [@j)ITi!J, ij@)I) .

Standard memory A B c D

Array memory A[O] A(1] A(2] A(3]

Proper use of the subscripts shortens programs and makes them easier to use.

Memory expansion Although there are 26 standard memories (A-Z), they can be expanded by changing program storage steps to memory. Memory expansion is performed by converting the 8 steps to one memory. *See page 90 for information on the number of program steps.

Number of memories 26 27 28 36 100 163 Number of steps 1103 1095 1087 1023 511 7

Memory is expanded in units of one. A maximum of 137 memories can be added for a maximum total of 163. Expansion is performed by pressing ~ followed by ~. a value representing the size of the expansion, and then @].

J Example I To expand the number of memories by 30 to bring the total to 56:

Defm 30_

Defm 30 30.

-41-

To check the current number of expanded memories, press~ followed by @ii!! and @!J. Defm J

.____ ___ 3_o~ . To initialize the number of memories (to return the number to 26) enter a zero for the value in the memory expansion sequence outlined above .

Defm 0 J ._______o.

*Though a maximum of 137 memories can be added, if a program has already been stored and the number of remaining steps is less than the desired expansion, an error (Mem ERROR) will be generated and expansion will be impossible.

*The expansion procedure (~@ii!! expansion value) can also be stored as a program.

Using expanded memories Expanded memories are used in the same manner as standard memories, and are referred to as variable Z[n] through variable A[n + 25], etc., as shown below:

Z[1]=Y[2]=X[3]= =A[26] (Defm 1) Z~2]=Y[3]=X[4]= ..... =A[27] (Defm 2)

Z[n]=Y[n+1]=X[n+2]= ..... =A[n+25] (Defm n) * n is the number of expanded memories.

For example, when two memories are added: Z[1]=Y[2]=X[3]= ..... =A[26] Z[2]=Y[3]=X[4]= ..... =A[27]

These memories are used in the same way as array-type memories, with a subscript be-ing appended to the name.

f Example f Inputting 123 in Z[2):

@@(I)~2@@ITJ~ )123

-42-

Defm 2 2.

ZC21= 123_

ZC21=123 123.

Recall memory data.

m I @@(I)@@ITJ2@@ITJ I

Z12L

] I Zl21 123. cautions when using array-type memories . When using array-type memories, a subscript is appended to an alphabetic character that represents a standard memory from A through Z. . Therefore, care must be taken to prevent overlap of memories. *The following shows a case in which array-type memories overlap with standard format memories. This situation should always be avoided.

The relation is as follows:

f ( ( ( ( ( ( 0--------f ( ( ( ( D------A BC DE FG X Y Z

Alo] Al 1 ] Al 2] A[ 3] A[ 4] A[ 5 ] A[ 6] A[23] A124] A125] A[26] A[27] 6[ o] 6[ 1 ] 6[ 2] 6[ 3] 6[ 4] 6[ 5] 6[22] 6[23] 6[24] 6[25] 6[26]

C[ o] C[ 1 ] C[ 2] C[ 3] q4] C[21] C[22] C[23] C[24] C[25]

G[O] G[17] G[18] G[19] G[20] G[21]

X[ 0 ] X[ 1 ] X[ 2 ] X[ 3 ] X[ 4 ] Y[O] Y[1] Y[2] Y[3]

Z[ 0 ] Z[ 1 ] Z[ 2 ]

Deleting memories . To delete all contents of variable memories (including expanded memories), press @iill followed by ~[@.

-43-

(2) Independent memories Addition and subtraction (to and from sum) results can be stored directly in memory. Results can also be totalized in memory, making it easy to calculate sums.

I Example I Inputting 123 to independent memory: r!B123

Recall memory data.

Add 25, subtract 12

251Ml12l@HE (Pressing 251:112~ provides same result.) Recall memory data.

*To clear memory contents, press @]!film@.

123_

123 123.

M= 123.

12 12.

M= 136.

*Addition/subtraction to or from sum in memory cannot be carried out with~. 00 and ~ keys in SD mode and LR mode.

-44- I

J

Difference between !film@ and ~. 00~. Both !film@ and~. 00~ can be used to input results into memory, however when the !film@ operation is used, previous memory contents are cleared. When~. 00~ is used, value is added or subtracted to or from present sum in memory.

@xample I Inputting 456 into memory "M" using !film@ procedure. Memory already contains value of 123:

r!B1231filID@ M= 123.

r!B4561filID[0 M= 456.

SB

IBID@ M= 456.

I Example I Inputting 456 into memory "M" using~- Memory already contains value of 123:

M= 123.

r!B4561Ml 456 456.

M= 579.

-45-

I Special functions Answer function This unit has an answer function that stores the result of the most recent calculation. Once a numeric value or numeric expression is entered and @I is pressed, the result (the answer in the case of numeric formulas) is stored by this function. To recall the stored value, press the[) key. When[) is pressed, "Ans" will appear on the display, and the value can be used in subsequent calculations. As the "Ans" function works just like any other memory, it will be referred to as "Ans memory" in subsequent sections of this manual.

I Example I 123 + 456 = 579 789-579 = 210

123 +456 579.

789-Ans_

789-Ans 210.

Numeric values with 12 digits for a mantissa and 2 digits for an exponent can be stored in the Ans memory. The Ans memory is not erased even if the power of the unit is turned OFF. Each time@!!, !!!i!I~. 1!1, !!!i!I~ and lfilQI a (a=A-Z) is pressed, the value in the Ans memory is replaced with the new value produced by the calculation execution. When execution of a calculation results in an error, however, the Ans memory retains its cur-rent value. Contents of Ans memory are not altered when~ a (a= A- Z) is used to recall contents of variable memory. Also, contents of Ans memory are not altered when variables are input when the variable input prompt is displayed.

Omitting the multiplication sign ( x) When inputting a formula as it is written, from left to right, it is possible to omit the mul-tiplication sign ( x) in the 'following cases: 1) Before the following functions:

sin, cos3 tan, sin 1, cos 1, tan 1, sinh, cosh, tanh, sinh 1, cosh 1, tanh 1, log, In, 10', eX, v, v, Pol (x, y), Rec (r, IJ) Ex. 2sin30, 101og1 .2, 2v'3, 2Pol(5, 12), etc.

-46-

2) Before fixed numbers, variables and memories: Ex. 271", 2AB, 3Ans, etc.

3) Before parentheses: Ex. 3(5+ 6), (A+ 1)(B-1), etc.

Continuous calculation function Even if calculations are concluded with the @I key, the result obtained can be used for further calculations. In this case, calculations are performed with 10 digits for the man-tissa which is displayed.

~xample J To calculate+ 3.14 continuing after 3 x 4 = 12:

(Continuing) ~3.14

[Example J To calculate 1 + 3 x 3 =:

(Continuing) f33~

3x4 12.

12./3.14_

12./3.14 3.821656051

1/3x3 1.

1/3 0.333333333

0 .333333333 x -0.999999999

Calculations performed with 1 O digits for mantissa.

This function can be used with Type A functions (x2, x-1, x!, see page 27), +, - , xY, V, and 0 ' ".

J Example J Squaring the result of 78 + 6 = 13:

13.

-47-

1~ (Continuing) ~~ 13.2_ J ~ 13.2 169.J

Replay function This function stores formulas that have been executed. After execution is complete, press-ing either the ~ or [E key will display the formula executed. Pressing ~ will display the formula from the beginning, with the cursor located under the first character. Pressing [E will display the formula from the end, with the cursor located at the space following the last character. After this, using the~ and [E to move the cursor, the for-mula can be checked and numeric values or commands can be changed for subsequent execution.

I Example I PD123t3456~

I Example I 4.12x3.58+6.4=21.1496 4.12x3.58-7.1 =7.6496

E4.12t33.5806.4~

-48-

123 x 456 56088.

123 x456

123 x 456 56088.

123 x 456_

4.12x3.58+6. -21.1496

1- 12 x 3.58+6.4_

[E[E[E[E 1- 4.12 x 3.58 6. -1

1::11.1 1-12x3.58-7.1_

~ 4.12x3.58-7. -7.6496

As with the number of input characters (see page 30), the replay function can accept input of up to 127 steps.

*The replay function is not cleared even when r!!J is pressed or when power is turned OFF, so contents can be recalled even after E is pressed.

~ PD123t3456~ 123 x 456 56088.

123 x 456_

'Replay function is cleared when mode or operation is switched.

Error position display function When an ERROR message appears during operation execution, the error can be cleared by pressing them key and the values or formula can be re-entered from the beginning. However, by pressing the~ or [E key, the ERROR message is cancelled and the cursor moves to the point where the error was generated.

I Example I 14 + O x 2.3 mistakenly input instead of 14 + 1 O x 2.3: ml14~0t32.3~ Ma ERROR

~(or [E)

-49-

14/0 x 2.3

I Cursor indicates where error is generated

!BOO!ffifil1 14/1'.e:x 2.3 J @] 14/10 x 2.3

3.22

Multistatement function The multistatement function (using colons to separate formulas or statements) availa. ble in program calculations can also be used for manual calculations.

The multistatement function allows formulas to be separated by colons (!filBITJ) to make consecutive, multiple statement calculations possible.

When @] is pressed to execute a formula input using the multistatement format, the formula is executed in order from the beginning.

Inputting "A" (!filB(1]) in place of the colon (!filBITJ) will display the calculation result up to that point during execution.

I Example I 6.9x123=848.7 123 _,_ 3.2 = 38.4375

PD123~006.9t~ (!]~[ZJ~(!]~3.2@] 6.9 xA J 848.7

l!ll!!I i

Appears on display when " _. " is used.

A/3.2 J 38.4375

*Even if "A" is not input at the end of a formula, the final result will be displayed. *Consecutive calculations containing multistatements cannot be performed.

123x456~5 L-1nvalid

Calculations can be performed while an intermediate result is displayed during execu-tion interrupted by " .A ".

I Example I 5 x 6 ..illl 7 x 8_ Ill

Sx6 30.

l!ll!!I Ill

-50-

~~ sin Ans_ l!ll!!I Ill

sin Ans @] 0.5 l!ll!!I Ill

. t operation is completed, press@] once again to execute. When interrup ....----------, I 7x8 56.

Ill

-51-

t Scientific function calculations [.l Trigonometric functions and inverse trigonometric functions Be sure to set the unit of angular measurement before performing trigonometric tune. tion and inverse trigonometric function calculations.

The unit of angular measurement (degrees, radians, grads) is set by pressing~ fol-lowed by a value from rn to !]]. (90 =~radians= 100 grads)

2

One~ a unit of angular measurement is set, it remains in effect until a new unit is set. Settings are not cleared when power is switched OFF.

This operation is invalid in the BASE-N mode. When in the BASE-N mode, make set-ting after pressing ~ followed by [[].

Example Operation Display (Lower) sin 6352 '41 = 0.897859012 ~rn -> " m "

~638528418~

cos ( -f rad)= 0.5 ~rn __, " rn "

tan( - 35gra) = -0.612800788

2sin 45 x cos 65 =0.597672477

sin- 10.5 = 30 (Determines x for sinx ~ 0.5)

cos- 1 v; =0.785398163 rad = 2- rad

4

!IITJllffiffiooa 3CD~

~rn __, "l!l" 2Et~45EtJ65~

L caJ be omitted. llffiffil!fil:)0.5~

t Can be entered as .5

~rn __,"Iii" llffiffi~ITJ112a2CD ~

allffiffioo~

-52-

0.897859012

0.5

-0.612800788

0.597672477

30.

0.785398163 0.249999999

-1 0 741 =36.53844577 tan =3632'18.4"

~rn __, "l!l" llffiffil!!m0.741~

llffiffi 'If the total number of digits for degrees/minutes/seconds ex-ceeds 11 digits, the high-order values (degrees and minutes) are given display priority, and any lower-order values are not displayed. However, the entire value is stored within the unit as a decimal value.

-1 -1 9) 2.5 x (sin 0.8- cos 0. 2.5EtITJllffiffil!fil:}0.81:1

= 6813' 13.53"

36.53844577 36a32a 18.4

Logarithmic and exponential functions The following operation is invalid in the BASE-N mode. When in the BASE-N mode, carry out calculation after pressing~ followed by[[].

Example

log 1.23 (log101.23) = 8.9905111x10- 2

ln90 (log90) = 4.49980967

log456 + ln456 = 0.434294481 (log/In ratio~ constant M)

10123 =16.98243652

Operation

1)1.23~

lli)90~

~456alli:l456~

~~1.23~ (To obtain the anti-logarithm of common logarithm 1.23)

e45 =90.0171313 I ~~4.5~ (To obtain the anti-logarithm of natural logarithm 4.5)

104.e-4 + 1.2 .102.3 = 422.5878667

(-3)4 =(-3) x(-3)x (-3)x(-3) =81

-34= -(3x3x3x3)= -81

5.623 = 52.58143837 1

\/123 (=1237) = 1.988647795

llffiffi~4Etllffiffi~l8]40 1.2Etllffiffi~2.3~

5.6~2.3~

71lffiffi~123~

-53-

Display

0.089905111

4.49980967

0.434294481

16.98243652

90.0171313

422.5878667

81.

-81.

52.58143837

1.988647795

(78-23)- 12 = 1.305111829x10- 21

2+3xV64 -4=10 203131!ffili)~641:14@1 10, *xY and V- given calculation priority over x and/.

2x 3_4

Permutation and combination Total number of permutations nPr=-n_!_ (n-r)!

Total number of combinations nCr- nl

rl (n-r)!

The following operation is invalid in the BASE-N mode. When in the BASE-N mode carry out calculation after pressing ~ followed by !]). '

Example Operation Display (Lower) Taking any four out of ten items and arranging them in a row, how many different ar-rangements are possible?

10P4=5040

Using any four numbers from 1 to 7, how many four-digit even numbers can be formed if none of the four digits con-sist of the same number? (~ of the total number of permutations will be even.)

7P4X ~=360 7

If any four items are removed from a total of 1 O items, how many different combinations of four items are possible?

10C4=210

If 5 class officers are being selected for a class of 15 boys and 10 girls, how many combinations are possible? At least one girl must be includ-ed in each group.

2sCs -1sCs = 50127

25@~51:115 @~5@]

-56-

-

5040.

360.

210.

50127.

1 other functio~s.

Fractions Fractions are input and displayed in the following order: integer, numerator, denominator~

Example Operation

.+31-=3~ 2~5Cl3~1~4@] 5 4 20 = 3.65 (Conversion to decimal)~

Fractions can be converted to decimals, and then converted back to fractions.

456 11 378=813 (Reduced) 3~456~78@]

(Continuing) llfilill~ Fractions and improper fractions which can be reduced become reduced fractions when the calculation command key is pressed. Press liillill~ to convert to improper fraction.

1 1 2578 + 4572 = 6.066202547 x 10- 4 1~2578Cl1~4572@]

when the total number of characters, including integer, numer-ator, denominator and delimiter mark exceeds 10, the input frac-tion is automatically displayed in decimal format.

1 2 x0.5=0.25 I

1 _g_= l 3 6

calculations containing both fractions and decimals are calcu-lated in decimal format.

1 ~2t1 ~3Cl1 ~4t 1~5@]

1~CD1~3CI1 ~40J@l

when parentheses are used in numerators or denominators, it is possible to carry out fractional calculations.

-58-

Display (Lower)

3.J13.J20, 3.65

6.066202547-04 (Norm mode)

0.25

~gineering symbol calculations I This unit allows engineering calculations utilizing engineering symbols. The Eng mode is specified by pressing ~c:J in the COMP mode(~[[)), LR mode (!If.ID), SD mode(~(]]) ("Eng" symbol appears on display). To exit from this mode, press 18 once again.

Operation Unit 103

I@)@ (=[I]) 106 I@)[[] ( = [[]) 109 liillJITl(=OO) 1012 liillJ@l (=W) 10-3 1@10 (=[!]) 10-6

I@)@] ( = (]]) 10-9

liilll@l ( =rn) 10-12 l@JCD (=III) 10-15

Example

999k (kilo)+ 25k (kilo) = 1.024M (mega)

10om (milli) x 5 (micro) = 500n (nano)

9 + 1O=0.9 = 900m (milli)

Unit symbol k (kilo) M (mega) G (giga) T (tera) m (milli) (micro) n (nano) p (pico) f (femto)

Operation

~c:J --> "Eng" 9991lfilill[K)Cl251lfilill[K)@l

-59-

9~10@] llfilill~

~

Display (Lower)

500."

900.m 0.9

900.m

I Binary, octal, decimal, hexadecimal calculations!. Binary, octal, decimal and hexadecimal calculations, conversions and logical operations are performed in the BASE-N mode (press ~ITJ).

The number system (2, 8, 10, 16) is set by respectively pressing @ID,!@, rnrn or @J. A corresponding symbol - "b", "o", "d" or "H" appears on the display.

Number systems are specified for specific values by pressing@. then the number sys-tem designator (b, o, d, or h), immediately followed by the value.

General function calculations cannot be performed in the BASE-N mode. Only integers can be handled in the BASE-N mode. If a calculation produces a result that includes a decimal value, the decimal portion is cut off.

If values not valid for the particular number system are used, attach the corresponding designator (b, o, d or h), or an error message will appear.

Number system Valid values Binary 0, 1 Octal 0, 1, 2, 3, 4, 5, 6, 7 Decimal 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Hexadecimal 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

To distinguish the A, B, C, D, E and Fused in the hexadecimal system from standard letters, they appear as shown in the chart below.

Key Display (Upper) 1?6.1 ( = IBJ) IA 00 (= 8) IB [}(= ~) c

mi(=~) ID 00 (= 1) IE (!] ( = []) IF

Negative numbers in binary, octal and hexadecimal are expressed as two's complements. ~mber of digits displayed in each number system

Number system Number of digits displayed Binary Up to 32 digits (8 digits x 4 blocks) 6ctal Up to 11 digits (8 digits+ 3 digits) Decimal Up to 10 digits Hexadecimal Up to 8 digits

-60-

.calculation range (in BASE-N mode) Binary Positive : 011111111111111111111111111111112:x2:0

Negative : 11111111111111111111111111111111 ~ x -~10000000000000000000000000000000

Octal Positive : 17777777777 ~ x ~ 0 Negative : 37777777777 ~ x ~ 20000000000

Decimal Positive : 2147483647~x~O Negative : -1 ~x~ -2147483648

Hexadecimal Positive : 7FFFFFFF~x~O Negative : FFFFFFFF~x~8ooooooo

Binary and octal block display In the binary mode, a maximum of 32 digits are displayed in 4 blocks of a digits. In the octal mode, a maximum of 11 digits are displayed in one block of 8 digits, and a second block of 3 digits.

@xample I In binary mode:

Block 4 Block 3 Block 2 Block 1 10000111 01100101 01000011 00100001

i..--------32 digits---------i

In octal mode:

Block 2 Block 1 012 34567012

In the binary mode, Block 1 is displayed immediately after calculation. Other blocks are displayed by pressing the~ key. The block number increments each time you press the~ key. The 4-digit symbol display at the upper right indicates the block presently being displayed. To reverse the order (shift from Block 4 to Block 3, etc.), press@~.

Indicates Block 1 presently displayed r---~~~~---..,i---.

1000011 CICICl~-00100001 b (Block 1)

-61-

Block 2

1000011 --;-Cl Cl. Cl .. 01000011 b (Block 2) ~

Block 3

1000011 .-Cl. Cl Cl-01100101 b (Block 3)

Block 4

1000011 .-1:11:11:1-10000111 b (Block 4)

1000011 CICICI ... 00100001 b (Returns to Block t)

1000011 C1C1CI,... 10000111 b (Returns to Block 4)

In the octal mode, Block 1 is displayed immediately after calculation. Block 2 displayed by pressing the~ key. The block display switches between Block 1 and Block 2 each time you press the~ key. The 2-digit symbol display at the upper right indicates the block presently being displayed.

012345670 .. -34567012 (Block l)

012345670 .... 012 0 (Block 2)

012345670 .... 34567012 0 (Returns to Block 1)

-62-

Binary, octal, decimal, hexadecimal conversions are two ways to perform reciprocal binary, octal, decimal and hexadecimal con-There versions.

conversion using number system specification key :Siue from a different number system input when a specific number system mode is be-ing used .

Example Operation Display (Lower)

What are the hexadecimal ffi!!] -+ "H" values for 123 10 and 10102?

What are the octal values for ~ -> "o" 1516 and 1100 2?

What are the binary values for ~ -> "b" 36 10 and 2C 16?

l!ffi!!J@)1231ili] @(fil10101ili!

l!ill!!J(fil 11001@

d

42 d 188 d

0000007b H OOOOOOOA H

...

00000025 0 ...

00000014

r:::::ICll:I

00100100 b

00101100 b

Conversion using number system mode key Calculation results can be converted to any specified number system by using the cor-responding number system mode key.

Example

How is 22 10 expressed in binary, octal and hexadecimal number systems?

Operation

~-> "d"

-63-

Display (Lower)

221ili] 22 d l!ffiJ 00010110 b

...

~ 00000026 0

~ 00000016 H

Negative expressions _____ E_x_a_m_p_le ____ +-___ O_;_p_er_a_li_o_n ___ -+ __ D_is..:.p_la--'y_(:..._L_ow.:..:e:::r)._. A

l!!!IDGJ How is 1100102 expressed as !!!] -+ "b" a negative?

~110010~ 1:::11:::11:1 ..

11001110 b

~ c11::::11:1

11111111 b

~ ..... "!

11111111 b

~ cu::11:1

11111111 b

How is 728 expressed as a mE!1 -+ "o" negative? ~72~

...

77777706 0

~ ...

377 0

How is 3A 16 expressed as a ffi!!l-+ "H" negative? ~3A~ FFFFFFC6 H

-64-

Basic arithmetic operations using binary, octal, decimal and hexadecimal values

Example

1238 xABC 16 = 37AF4ie =22808410

1F2D 16 -100 10 = 7881 1o = 1EC9 16

Operation

~GJ 00!1 -+ "b"

10111011010~

ffi!!1-+ "H" B47IDDF~

l!ffiill@J 123EtABC~ @)

l!ffiillllil1F2DID100~ ffi!!l

76549+1210=334.333333310 @)-+ "d" =5168

Display (Lower)

CICICI

00110001 b

OOOOOA68 H

00037AF4 H 228084 d

7881 d 00001EC9 H

334 d

~ 00000516 0

*Calculation results are displayed with the decimal portion cut off.

123410+ 1EF15+ 24a =2352 8 = 125810

l!ffiill@J 1234Dl!ffiillllil 1EFD24~

@)

*For mixed basic arithmetic operations, multiplication and divi-sion are given priority over ~ddition and subtraction.

-65-

Cl 00002352 0

1258 d

Logical operations ,. Logical operations ~re per.formed through logical products (and), logical sums (or), '' gat1on (Not), exclusive logic sums (xor), and negation of exclusive logical sums ( Ile, -------;:=:::::-;-:-------i_:__:__-::--_:_ _ __:___:_==;..:::....:::.~::....:::=~xnnor).

Example Operation Display (Lower)

191s AND 1A15= 1815

11102 AND 36a= 11102

23a OR 61a=63a

10102 AND (A1s OR 715) = 10102

ffi!!J -+ "H"

~ ---+. "b" 1110@~@@]36~

[Q!] -+ "o" 23@~61~

ffi!!I -+ "H" 120@~@lli)1101 ~

~ -+ "b" 101 O@~ITJ@lliJA

@~@lli]7[IJ~

IH!!J -+ "H"

2A1s XNOR 5D15 = FFFFFF8815 1H!!J -+ "H" 2A@~5D~

Negation of 12348 [Q!J -+ "o" ~1234~

Negation of 2FFFED 16 li!!iJ -+ "H" ~2FFFED~

-66-

00000018 H

c11:11::::1 00001110 b

...

00000063 0

0000012d H

CICICI 00001010 b

00000006 H

FFFFFF88 H

...

77776543 0

FFd00012 H

ll[]!istical calculations I . unit can be used to make statistical calculations including standard deviation in the ~srnode, and regression calculation in the LR mode.

istandard deviation In the SD mode, calculations including 2 types of standard deviation formulas, mean, number of data, sum of data, and sum of squares can be performed.

Data input 1. press @00 to specify the SD mode. 2. press lfil!]~~ to clear the statistical memories. 3. Input data, pressing @I key (=~)each time a new piece of data is entered. For nega-

tive values, press !Bl followed by @).

~ Data: 10, 20, 30 Key operation: 10@120@130@1

When multiples of the same data are input, two different entry methods are possible:

~Data: 10, 20, 20, 30 Key operation: 10@120@1@130@1

The previously entered data is entered again each time the @I key is pressed without entering data (in this case 20 is re-entered).

@mple 2 J Data: 10, 20, 20, 20, 20, 20, 20, 30 Key operation: 10@120@[I)6@130@1

By pressing @ and then entering a semicolon followed by a value that represents the number of items the data is repeated (6, in this case) and the @I key, the multiple data entries (for 20, in this case) are made automatically.

Deleting input data There are various ways to delete value data, depending on how and where it was entered.

@xample 1 J 40@120@130@150@1 To delete 50, press @@.

[Example 2 J 40@120@130@150@1 To delete 20, press 20 @@.

JExample 3 J 30@150@1120@1Il To delete 120 @[I), press f!i.

-67-

I Example 41 30[Q!)SO[Q!)1201!E@[I)31 To delete 120 l!E@[I) 31, press m!J.

I Examples I 30[Q!)SO[Q!)1201!E@[I)31 IQ!) To delete 120 l!E@ITJ 31 IQ!), press l!E@@J.

I Examples I 50[Q!)1201!E@[I)31 [Q!)40[Q!)30[Q!) To delete 120 l!E@ITJ 31 IQ!), press 120 l!E@ITJ 31 l!E@@J.

I Example 71 0101Q!J020IQ!J030[Q!) To delete 0 20 IQ!), press 0 20 ~~l!E@@J.

Note: You need to press ~~ to delete a calculation result, such as v'20.

I Examples I 010IQ!J020[Q!)[D30[Q!) To delete 0 20 !QTI, press 0 20 l!EITJIBI 1 IQ!).

Performing calculations The following procedures are used to perform the various standard deviation calculations.

Key operation Result Ml~ Population standard deviation xan ] =c:J

@=@) 00 =@)

~=CD ~ =[]] 0J =(]]

M@~ Sample standard deviation xan-1 MOO~ Mean

M~~ Sum of squares of data M~~ Sum of data

Milll~ Number of data Standard deviation and mean calculations are performed as shown below:

Standard deviation

f (x -x)2 i=1 l

n

f (x-x)2 i=1 I n-1

Mean n

Ex; Ex i=1 x n n

n

n-1

-68-

[ Using the entire data of a finite] population to estimate the stan-dard deviation for the population.

[ Using sample data for a population] to estimate the standard deviation for the population.

Example Operation Display (Lower) oata 55, 54, 51, 55, 53, 53, ~(]]_,"SD" 54, 52 (Memory cleared) M[gjl~

55[Q!)54[Q!)51[Q!)55[Q!)53 [Q!)[Q!J 54 IQ!) 52 IQ!) 52.

Results can be obtained in any order desired.

I (Standard deviation an) Ml~ 1.316956719 (Standard deviation an-1)M@~ 1.407885953

(Mean x) MOO~ 53.375 (Number of data n) M0J~ 8.

(Sum total Ex) M~~ 427. (Sum of squares l.:x 2 ) M~~ 22805.

What is deviation of the unbi- (Continuing) M@i!E~~ 1.982142857 ased variance, the difference 551::1MOO~ 1.625 between each datum, and the mean of the above data? 541::1MOO~ 0.625

51 l::IMOO~ -2.375

What is x and an -1 for the fol- M[gjl~ lowing table? 110@[I)10[Q!) 110. Class no. Value Frequency 1301!E@[I)31 IQ!) 130.

1 110 10 1501!E@[I)24[Q!) 150. 2 130 31 3 150 24 170 [Q!)[Q!) 170. 4 170 2 190 [Q!)[Q!J[Q!) 190. 5 190 3

M0J~ 70. MOO~ 137. 7142857 M@~ 18.42898069

-69-

Regression calculation In the LR mode, calculations including linear regression, logarithmic regression, exponen-tial regression, and power regression can be performed.

Linear regression Linear regression calculations are carried out using the following formula: y =A+ Bx. Data input 1. Press ~(]] to specify the LR mode. 2. Press ~~~ to clear the statistical memories. 3. Input data in the following format:

0 @]

*When multiples of the same data are input, two different entry methods are possible:

I Example 1 I Data: 10/20, 20/30, 20/30, 40/50 Key operation: 10020@]

20030@] @] 40050@]

The previously entered data is entered again each time the @] key is pressed (in this case 20/30 is re-entered).

I Example 2 I Data: 10/20, 20/30, 20/30, 20/30, 20/30, 20/30, 40/50 Key operation: 10020@]

20030liE!ill0]5@] 40050@]

By pressing liE!ill and then entering a semicolon followed by a value that represents the number of times the data is repeated (5, in this case) and the@] key, the multiple data entries (for 20/30, in this case) are made automatically. Deleting input data There are various ways to delete value data, depending on how and where it was entered. I Example 1 J 10040@]

20020@] 30030@] 40050

To delete 40 0 50, press E.

I Example 2 J 10040@] 20020@] 30030@] 40050@]

To delete 40 0 50 @], press liE!ill.

-70-

~ To delete 20 0 20 @], press 20 0 20 liE!ill.

~010040@] ~020020@]

030030@1 040050@]

To delete 0 20 0 20 @], press 0 20 ~~0 20 liE!ill.

~ To delete 0 20 0 20 @], press 0 20 0 20 liE!illOJIBJ 1 @].

Performing calculations The following procedures are used to perform the various linear regression calculations.

Key operation Result lfilf)[AJ~ Constant term of regression A (A] =lfilID

lfilf)l]J~ Regression coefficient B 00 =@J lfilf)[D~ Correlation coefficient r l:D=ITJ lfilf)~~ Estimated value of x ~=ITJ lfilf)[2]~ Estimated value of y !2l=0

The regression formula is y =A+ Bx. The constant term of regression A, regression coeffi-cient B, correlation coefficient r, estimated value of x, and estimated value of y are calcu-lated as shown below:

A= Ey-BEx n

r= nExy-ExEy

B nExy- ExEy n Ex2 - (Ex)2

J[nEx2 -(Ex)2] [nEy 2 -(Ey)2]

.Y=A+Bx x= y-A B

-71-

Example

Temperature and length of a steel bar

Temp. Length 10C 1003mm 15C 1005mm 20C 1010mm 25C 1011mm 30C 1014mm

Using this table, the regres-sion formula and correlation coefficient can be obtained. Based on the coefficient for-mula, the length of the steel bar at 18C and the tempera-ture at 1 OOOmm can be esti-mated. Furthermore, the critical coefficient (r2) and covariance

( Exy-nxY) n-1

can also be calculated.

Logarithmic regression

Operation

~[]] __, "LR" (Memory clear) ~~@)

10010031Q!) 15010051Q!) 20010101Q!) 25010111Q!) 30010141Q!)

(Constant term A) ~IA]@) (Regression coefficient B) ~[[]@) (Correlation coefficient r) ~0@1

(Length at 18C) 18~(2)@) (Temperature at 1000mm)

1000~00@1 (Critical coefficient)~01iH!ffi~@J (Covariance) (]]~l:l~(fil

f3~~f3~~rn~m ~(fill:l 1 CIJ@J

11

Display (L ower) -

10. 15. 20. 25. 30.

997.4 0.56

0.982 607368 1007.48

4.642 0.965

857143 517241

35.

Logarithmic regression calculations are carried out using the following formula: y=A+Blnx.

Data input 1. Press ~[]] to specify the LR mode. 2. Press ~~@) to clear the statistical memories. 3. Input data in the following format:

lliil 0 IQ!) *To make multiple entries of the same data, follow procedures described for line ar regres-sion, however always press lliil before inputting x data.

Deleting input data To delete input data, follow the procedures described for linear regression, b to use the lliil key when specifying x data for deletion. I Example 1 I To delete lliil 10 0 20 IQ!), press lliil 10 @1~0 20 liH!ffi.

-72-

ut be sure

,.....--

~ To delete [Iii) 1 O 0 20 IQ!), press I lliiJ 10 0 20 liH!ffiQJIB 1 IQ!J. .performing calculations The following procedures are used to perform the various calculations. ..-- Key operation r-lfil1)[IJ@J

lfil1)[[]@1 i-lfil1)0@1

ylfil1)00@JliH!ffi~~@) [I@x~(2)@)

Result Con slant term of regression A Reg ression coefficient B Corr elation coefficient r Esti mated value of x Esti mated value of y

[IJ=lfilID [[]=IBID 0=(]] OO=CIJ (2)=0

If we assume that lnx=x, the logari thmic regression formula y =A+ Blnx becomes the Therefore, the formulas for constant term A, regres-

coefficient r are identical for logarithmic and linear linear regression formula y =a+ bx. sion coefficient B and correlation regression.

A number of logarithmic regression calculation results differ from those produced by linear regression. Note the following:

Linear regression Logarithmic r egression Ex Elnx Ex2 E(lnx) 2 Exy Elnx

Example

xi yi 29 1.6 50 23.5 74 38.0

103 46.4 118 48.9

Through logarithmic regres-sion of the above data, the regression formula and corre-lation coefficient are obtained. Furthermore, respective esti-mated values y and x can be obtained for xi= 80 and yi = 73 using the regression formula.

Operation

M ~(]) --+ "LR"

( (

~~@) lliil2901.61Q!)

[Iii)50023.51Q!) [Iii)74038.0IQ!)

[Iii)103046.4@!) [Iii)118048.9@!)

(Constant term A) ~IA]@) Regression coefficient B) ~[[]@) Correlation coefficient r) ~0@1

(.Y when xi=80) llii)80~(21@) (f when yi= 73) 73~00@JliH!ffi~~@)

-73-

Display (Lower)

3.36729583 3.912023005 4.304065093 4.634728988 4. 770684624

-111.1283976 34.02014749 0.994013946 37.94879482

224.1541314

Exponential regression Exponential regression calculations are carried out using the following formula: y=Ae8 x (lny=lnA+Bx) Data input 1. Press ~rn to specify the LR mode. 2. Press ~~Ifill to clear the statistical memories. 3. Input data in the following format:

[Dllii] [QI] *To make multiple entries of the same data, follow procedures described for linear regres. sion, however always press lliil before inputting y data.

Deleting input data To delete input data, follow the procedures described for linear regression, but be sure to use the lliiJ key when specifying y data for deletion.

I Example 1 I To delete 10 [Dllii] 20 [QI], press lliil 20 lfil] 10 CD~liE!ffi@Y.

I Example 2 I To delete 10 [Dllii] 20 [QI], press 10 [Dllii] 20 liE!ffiITl1811 [QI].

Performing calc