Casio ALGEBRA FX 2.0 User manual

19990401
Manual Calculations
2-1 Basic Calculations
2-2 Special Functions
2-3 Specifying the Angle Unit and Display Format
2-4 Function Calculations
2-5 Numerical Calculations
2-6 Complex Number Calculations
2-7 Binary, Octal, Decimal, and Hexadecimal Calculations
2-8 Matrix Calculations
Chapter 2

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2-1-1
Basic Calculations
2-1 Basic Calculations
kk
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kArithmetic Calculations
•Enter arithmetic calculations as they are written, from left to right.
•Use the -key to input the minus sign before a negative value.
•Calculations are performed internally with a 15-digit mantissa. The result is rounded to a
10-digit mantissa before it is displayed.
•For mixed arithmetic calculations, multiplication and division are given priority over
addition and subtraction.
Example Operation
23 + 4.5 – 53 = –25.5 23+4.5-53w
56 ×(–12) ÷(–2.5) = 268.8 56*-12/-2.5w
(2 + 3) ×102= 500 (2+3)*1E2w*1
1 + 2 – 3 ×4 ÷5 + 6 = 6.6 1+2-3*4/5+6w
100 – (2 + 3) ×4 = 80 100-(2+3)*4w
2 + 3 ×(4 + 5) = 29 2+3*(4+5w*2
(7 – 2) ×(8 + 5) = 65 (7-2)(8+5)w*3
6= 0.3 6/(4*5)w*4
4×5
(1 + 2i) + (2 + 3i) = 3 + 5i(b+c!a(i))+(c+
d!a(i))w
(2 + i) ×(2 – i) = 5 (c+!a(i))*(c-!a(i)
)w
*1(2+3)E2 does not produce the correct
result. Be sure to enter this calculation as shown.
*2Final closed parentheses (immediately before
operation of the wkey) may be omitted, no
matter how many are required.
*3A multiplication sign immediately before an open
parenthesis may be omitted.
*4This is identical to 6 /4 /5 w.

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2-1-2
Basic Calculations
*1Displayed values are rounded off to the place
you specify.
kk
kk
kNumber of Decimal Places, Number of Significant Digits, Normal
Display Range [SET UP]- [Display] -[Fix] /[Sci] /[Norm]
•Even after you specify the number of decimal places or the number of significant digits,
internal calculations are still performed using a 15-digit mantissa, and displayed values
are stored with a 10-digit mantissa. Use Rnd of the Numeric Calculation Menu (NUM)
(page 2-4-1) to round the displayed value off to the number of decimal place and number
of significant digit settings.
•Number of decimal place (Fix) and number of significant digit (Sci) settings normally
remain in effect until you change them or until you change the normal display range
(Norm) setting.
○○○○○
Example 100 ÷6 = 16.66666666...
Condition Operation Display
100/6w16.66666667
4 decimal places u3(SET UP) cccccccccc
*1
1(Fix)ewiw16.6667
5 significant digits u3(SET UP) cccccccccc
*1
2(Sci)fwiw1.6667E+01
Cancels specification u3(SET UP) cccccccccc
3(Norm)iw16.66666667

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2-1-3
Basic Calculations
○○○○○
Example 200 ÷7 ×14 = 400
Condition Operation Display
200/7*14w400
3 decimal places u3(SET UP) cccccccccc
1(Fix)dwiw400.000
Calculation continues 200/7w28.571
using display capacity *Ans ×
of 10 digits 14w400.000
• If the same calculation is performed using the specified number of digits:
200/7w28.571
The value stored K5(NUM)e(Rnd)w28.571
internally is cut off to *Ans ×
the number of 14w399.994
decimal places you
specify.
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kk
kCalculation Priority Sequence
This calculator employs true algebraic logic to calculate the parts of a formula in the following
order:
1Coordinate transformation Pol (x, y), Rec (r, θ )
Differentials, quadratic differentials, integrations, Σcalculations
d/dx, d2/dx2, ∫dx, Σ, Mat, Solve, FMin, FMax, List→Mat, Seq, Min, Max, Median, Mean,
Augment, Mat →List, P(, Q(, R(, t(, List
2Type A functions
With these functions, the value is entered and then the function key is pressed.
x2, x–1, x!, °’ ”, ENG symbols, angle unit o, r, g
3Power/root ^(xy), x
4Fractions ab/c
5Abbreviated multiplication format in front of π, memory name, or variable name.
2π, 5A, Xmin, F Start, etc.
6Type B functions
With these functions, the function key is pressed and then the value is entered.
, 3, log, In, ex, 10x, sin, cos, tan, sin–1, cos–1, tan–1, sinh, cosh, tanh, sinh–1, cosh–1,
tanh–1, (–), d, h, b, o, Neg, Not, Det, Trn, Dim, Identity, Sum, Prod, Cuml, Percent, AList,
Abs, Int, Frac, Intg, Arg, Conjg, ReP, ImP

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2-1-4
Basic Calculations
7Abbreviated multiplication format in front of Type B functions
2, A log2, etc.3
8Permutation, combination nPr, nCr
9×, ÷
0+, –
!Relational operators >, <, ≥, ≤
@Relational operators =, G
#and (bit operation)
$xnor, xor (bit operations)
%or (bit operation)
^And (logical operation)
Or (logical operation)
○○○○○
Example 2 + 3 ×(log sin2π2+ 6.8) = 22.07101691 (angle unit = Rad)
1
2
3
4
5
6
#When functions with the same priority are used
in series, execution is performed from right to
left.
exIn →ex{In( )}
120 120
Otherwise, execution is from left to right.
#Compound functions are executed from right to
left.
#Anything contained within parentheses receives
highest priority.

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2-1-5
Basic Calculations
# Other errors can occur during program
execution. Most of the calculator’s keys
are inoperative while an error message is
displayed.
Press ito clear the error and display
the error position (see page 1-3-4).
# See the “Error Message Table” on page α-1-1
for information on other errors.
kMultiplication Operations without a Multiplication Sign
You can omit the multiplication sign (×) in any of the following operations.
• Before coordinate transformation and Type B functions (1and 6on page 2-1-3), except
for negative signs
○○○○○
Example 2sin30, 10log1.2, 2 , 2Pol(5, 12), etc.
•Before constants, variable names, memory names
○○○○○
Example 2π, 2AB, 3Ans, 3Y1, etc.
•Before an open parenthesis
○○○○○
Example 3(5 + 6), (A + 1)(B – 1), etc.
kOverflow and Errors
Exceeding a specified input or calculation range, or attempting an illegal input causes an
error message to appear on the display. Further operation of the calculator is impossible
while an error message is displayed. The following events cause an error message to appear
on the display.
•When any result, whether intermediate or final, or any value in memory exceeds
±9.999999999 ×1099 (Ma ERROR).
•When an attempt is made to perform a function calculation that exceeds the input range
(Ma ERROR).
•When an illegal operation is attempted during statistical calculations (Ma ERROR). For
example, attempting to obtain 1VAR without data input.
• When an improper data type is specified for the argument of a function calculation
(Ma ERROR).
•When the capacity of the numeric value stack or command stack is exceeded (Stack
ERROR). For example, entering 25 successive (followed by 2 +3 *4 w.
•When an attempt is made to perform a calculation using an illegal formula (Syntax
ERROR). For example, 5 ** 3 w.

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•When you try to perform a calculation that causes memory capacity to be exceeded
(Memory ERROR).
•When you use a command that requires an argument, without providing a valid argument
(Argument ERROR).
•When an attempt is made to use an illegal dimension during matrix calculations
(Dimemsion ERROR).
• When an attempt is made to perform a calculation that has a real number argument and
produces a complex number solution, while “Real” is selected for the Complex Mode
setting on the SET UP Screen (Non-Real ERROR).
kMemory Capacity
Each time you press a key, either one byte or two bytes is used. Some of the functions that
require one byte are: b, c, d, sin, cos, tan, log, In, , and π. Some of the functions that
take up two bytes are d/dx(, Mat, Xmin, If, For, Return, DrawGraph, SortA(, PxIOn, Sum, and
an+1.
2-1-6
Basic Calculations
#As you input numeric values or commands,
they appear flush left on the display.
Calculation results, on the other hand, are
displayed flush right.
#The allowable range for both input and output
values is 15 digits for the mantissa and two
digits for the exponent. Internal calculations
are also performed using a 15-digit mantissa
and two-digit exponent.

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2-2 Special Functions
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kCalculations Using Variables
Example Operation Display
193.2aav(A)w193.2
193.2 ÷23 = 8.4 av(A)/23w8.4
193.2 ÷28 = 6.9 av(A)/28w6.9
kk
kk
kMemory
uVariables
This calculator comes with 28 variables as standard. You can use variables to store values
you want to use inside of calculations. Variables are identified by single-letter names, which
are made up of the 26 letters of the alphabet, plus rand θ . The maximum size of values that
you can assign to variables is 15 digits for the mantissa and 2 digits for the exponent.
uTo assign a value to a variable
[value] a[variable name] w
○○○○○
Example To assign 123 to variable A
Abcdaav(A)w
○○○○○
Example To add 456 to variable A and store the result in variable B
Aav(A)+efgaa
l(B)w
2-2-1
Special Functions
# Variable contents are retained even when
you turn power off.

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uTo display the contents of a variable
○○○○○
Example To display the contents of variable A
Aav(A)w
uTo cl ear a variable
○○○○○
Example To clear variable A
Aaaav(A)w
uTo assign the same value to more than one variable
[value]a[first variable name*1]K6(g)6(g)4(SYBL)d(~) [last variable
name*1]w
○○○○○
Example To assign a value of 10 to variables A through F
Abaaav(A)
K6(g)6(g)4(SYBL)d(~)
at(F)w
uFunction Memory [OPTN]-[FMEM]
Function memory (f1~f20) is convenient for temporary storage of often-used expressions. For
longer term storage, we recommend that you use the GRPH •TBL Mode for expressions and
the PRGM Mode for programs.
•{Store}/{Recall}/{fn}/{SEE} ... {function store}/{function recall}/{function area specification
as a variable name inside an expression}/{function list}
2-2-2
Special Functions
*1 You cannot use “r” or “
θ ” as a variable name.

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uTo st ore a function
○○○○○
Example To store the function (A+B) (A–B) as function memory number 1
(av(A)+al(B))
(av(A)-al(B))
K6(g)5(FMEM)
b(Store)bw
uTo recall a function
○○○○○
Example To recall the contents of function memory number 1
K6(g)5(FMEM)
c(Recall)bw
uTo di splay a list of available functions
K6(g)5(FMEM)
e(SEE)
2-2-3
Special Functions
#Ifthe function memory number to which you
store a function already contains a function, the
previous function is replaced with the new one.
#The recalled function appears at the current
location of the cursor on the display.

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2-2-4
Special Functions
uTo delete a function
○○○○○
Example To delete the contents of function memory number 1
AK6(g)5(FMEM)
b(Store)bw
•Executing the store operation while the display is blank deletes the function in the
function memory you specify.
uTo use stored functions
○○○○○
Example To store x3+ 1, x2+ xinto function memory, and then graph:
y= x3+ x2+ x+ 1
Use the following View Window settings.
Xmin = – 4, Xmax = 4, Xscale = 1
Ymin = –10, Ymax = 10, Yscale = 1
u3(SET UP)c1(Y=)i
AvMd+bK6(g)5(FMEM)b(Store)bw(stores (x3+ 1))
iAvx+v5(FMEM)b(Store)cw(stores (x2+ x))
iAK6(g)6(g)2(SKTCH)b(Cls)w
2(SKTCH)e(GRAPH)b(Y=)
K6(g)5(FMEM)d(fn)b+
5(FMEM)d(fn)cw
•For full details about graphing, see “5. Graphing”.

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kk
kk
kAnswer Function
The Answer Function automatically stores the last result you calculated by pressing
w(unless the wkey operation results in an error). The result is stored in the answer
memory.
uTo use the contents of the answer memory in a calculation
○○○○○
Example 123 + 456 = 579
789 – 579 = 210
Abcd+efgw
hij-!-(Ans)w
kk
kk
kPerforming Continuous Calculations
Answer memory also lets you use the result of one calculation as one of the arguments in
the next calculation.
○○○○○
Example 1 1 ÷3 =
1 ÷3 ×3 =
Ab/dw
(Continuing)*dw
Continuous calculations can also be used with Type A functions (x2,x-1,x!, page 2-1-3), +,
–, ^(xy), x, °’ ”, etc.
2-2-5
Special Functions
#The largest value that the answer memory
can hold is 15 digits for the mantissa and 2
digits for the exponent.
# Only numeric values and calculation results
can be stored in answer memory.
# Answer memory contents are not cleared
when you press the Akey or when you
switch power off.
#Answer memory contents are not changed
by an operation that assigns values to value
memory (such as: faav(A)w).

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kStacks
The unit employs memory blocks, called stacks , for storage of low priority values and
commands. There is a 10-level numeric value stack , a 26-level command stack , and a 10-
level program subroutine stack . An error occurs if you perform a calculation so complex that it
exceeds the capacity of available numeric value stack or command stack space, or if
execution of a program subroutine exceeds the capacity of the subroutine stack.
○○○○○
Example
2-2-6
Special Functions
1
2
3
4
5
b
c
d
e
f
g
h
2
3
4
5
4
×
(
(
+
×
(
+
...
...
Numeric Value Stack Command Stack
#Calculations are performed according to the pri-
ority sequence. Once a calculation is executed,
it is cleared from the stack.
#Storing a complex number takes up two numeric
value stack levels.
#Storing a two-byte function takes up two
command stack levels.

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kUsing Multistatements
Multistatements are formed by connecting a number of individual statements for sequential
execution. You can use multistatements in manual calculations and in programmed calcula-
tions. There are two different ways that you can use to connect statements to form
multistatements.
•Colon (:)
Statements that are connected with colons are executed from left to right, without stopping.
•Display Result Command (^^
^^
^)
When execution reaches the end of a statement followed by a display result command, execu-
tion stops and the result up to that point appears on the display. You can resume execution by
pressing the wkey.
○○○○○
Example 6.9 ×123 = 848.7
123 ÷3.2 = 38.4375
Abcdaav(A)
!J(PRGM)6(g)6(g)3(:)g.j
*av(A)!J(PRGM)4(^)
av(A)/d.cw
w
2-2-7
Special Functions
#The final result of a multistatement is always
displayed, regardless of whether the
calculation ends with a display result
command. Example : 123 ×456: ×5
Invalid
#You cannot construct a multistatement in
which one statement directly uses the result
of the previous statement.

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2-3 Specifying the Angle Unit and Display
Format
Before performing a calculation for the first time, you should use the SET UP screen to
specify the angle unit and display format.
kk
kk
kSetting the Angle Unit [SET UP]- [Angle]
1. On the Set Up screen, highlight “Angle”.
2. Press the function key for the angle unit you want to specify, then press i.
•{Deg}/{Rad}/{Gra} ... {degrees}/{radians}{grads}
•The relationship between degrees, grads, and radians is shown below.
360°= 2πradians = 400 grads
90°= π/2 radians = 100 grads
kk
kk
kSetting the Display Format [SET UP]- [Display]
1. On the Set Up screen, highlight “Display”.
2. Press the function key for the item you want to set, then press i.
•{Fix}/{Sci}/{Norm}/{Eng} ... {fixed number of decimal places specification}/
{number of significant digits specification}/{normal display}/{Engineering Mode}
uTo specify the number of decimal places (Fix)
○○○○○
Example To specify two decimal places
1(Fix) cw
Press the function key that corresponds to the
number of decimal places you want to specify
(
n = 0 to 9).
2-3-1
Specifying the Angle Unit and Display Format
#Displayed values are rounded off to the
number of decimal places you specify.

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uTo specify the number of significant digits (Sci)
○○○○○
Example To specify three significant digits
2(Sci) dw
Press the function key that corresponds
to the number of significant digits you
want to specify (
n = 0 to 9).
uTo specify the normal display (Norm 1/Norm 2)
Press 3(Norm) to switch between Norm 1 and Norm 2.
Norm 1: 10–2 (0.01)>|x|, |x| >1010
Norm 2: 10–9 (0.000000001)>|x|, |x| >1010
Ab/caaw(Norm 1)
(Norm 2)
uTo specify the engineering notation display (Eng Mode)
Press 4(Eng) to switch between engineering notation and standard notation. The
indicator “/E” is on the display while engineering notation is in effect.
You can use the following symbols to convert values to engineering notation, such as
2,000 (= 2 × 103) →2k.
E (Exa) × 1018 m (milli) × 10–3
P (Peta) × 1015 µ (micro) × 10–6
T (Tera) × 1012 n (nano) × 10–9
G (Giga) × 109p (pico) × 10–12
M (Mega) × 106f (femto) × 10–15
k (kilo) × 103
2-3-2
Specifying the Angle Unit and Display Format
#Displayed values are rounded off to the number
of significant digits you specify.
#Specifying 0 makes the number of significant
digits 10.
#The engineering symbol that makes the
mantissa a value from 1 to 1000 is automatically
selected by the calculator when engineering
notation is in effect.

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2-4 Function Calculations
kFunction Menus
This calculator includes five function menus that give you access to scientific functions not
printed on the key panel.
•The contents of the function menu differ according to the mode you entered from the Main
Menu before you pressed the Kkey. The following examples show function menus that
appear in the RUN •MAT Mode.
uu
uu
uNumeric Calculations (NUM) [OPTN]-[NUM]
•{Abs} ... {select this item and input a value to obtain the absolute value of the value.}
•{Int}/{Frac} ... select the item and input a value to extract the {integer}/{fraction} part.
•{Rnd} ... {rounds off the value used for internal calculations to 10 significant digits
(to match the value in the Answer Memory), or to the number of decimal places (Fix)
and number of significant digits (Sci) specified by you.}
•{Intg} ... {select this item and input a value to obtain the largest integer that is not greater
than the value.}
•{E-SYM} ... {engineering symbol}
•{m}/{µ}/{n}/{p}/{f} ... {milli (10–3)}/{micro (10–6)}/{nano (10–9)}/{pico (10–12)}/{femto
(10–15)}
•{k}/{M}/{G}/{T}/{P}/{E} ... {kilo (103)}/{mega (106)}/{giga (109)}/{tera (1012)}/{peta
(1015)}/{exa (1018)}
uu
uu
uProbability/Distribution Calculations (PROB) [OPTN]-[PROB]
•{x!} ... {press after inputting a value to obtain the factorial of the value.}
•{nPr}/{nCr} ... {permutation}/{combination}
•{Ran#}... {pseudo random number generation (0 to 1)}
•{P(}/{Q(}/{R(} ... probability {P(t)}/{Q(t)}/{R(t)}
•{t(} ... {value of normalized variate t(x)}
2-4-1
Function Calculations

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uu
uu
uHyperbolic Calculations (HYP) [OPTN]-[HYP]
•{sinh}/{cosh}/{tanh} ... hyperbolic {sine}/{cosine}/{tangent}
•{sinh–1}/{cosh–1}/{tanh–1} ... inverse hyperbolic {sine}/{cosine}/{tangent}
uu
uu
uAngle Units, Coordinate Conversion, Sexagesimal Operations (ANGL)
[OPTN]-[ANGL]
•{°}/{r}/{g} ... {degrees}/{radians}/{grads} for a specific input value
•{°’ ”}... {specifies degrees (hours), minutes, seconds when inputting a degrees/minutes/
seconds value}
•{'DMS} ... {converts decimal value to sexagesimal value}
•{Pol(}/{Rec(} ... {rectangular-to-polar}/{polar-to-rectangular} coordinate conversion
uu
uu
uInstant Functions
•{ °’ ”} ... {converts decimal value to degrees/minutes/seconds value}
•{ENG}/{ENG} ... shifts the decimal place of the displayed value three digits to
the {left}/{right} and {decreases}/{increases} the exponent by three.
When you are using engineering notation, the engineering symbol is also changed
accordingly.
•The { °’ ” }, {ENG} and { ENG} menu operations are available only when there is a
calculation result on the display.
kk
kk
kAngle Units
To change the angle unit of an input value, first press K3(ANGL). On the pull-up
menu that appears, select “°”, “r”, or “g”.
•Be sure to specify Comp for Mode in the SET UP screen.
Example Operation
To convert 4.25 rad to degrees: u3(SET UP)cccc1(Deg)i
243.5070629 4.25K6(g)3(ANGL)c(r)w
47.3°+ 82.5rad = 4774.20181° 47.3+82.5K6(g)3(ANGL)c(r)w
2-4-2
Function Calculations
# Once you specify an angle unit, it remains
in effect until you specify a different one.
The specification is retained even if you turn
power off.

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kk
kk
kTrigonometric and Inverse Trigonometric Functions
•Be sure to set the angle unit before performing trigonometric function and inverse
trigonometric function calculations.
•Be sure to specify Comp for Mode in the SET UP screen.
Example Operation
sin 63°= 0.8910065242 u3(SET UP)cccc1(Deg)i
s63w
π
cos (–– rad) = 0.5 u3(SET UP)cccc2(Rad)i
3c(!E(π)/d)w
tan (– 35gra) = – 0.6128007881
u3(SET UP)cccc3(Gra)i
t-35w
2 •sin 45°×cos 65°= 0.5976724775
u3(SET UP)cccc1(Deg)i
2*s45*c65w*1
cosec 30°= 1 = 2 1/s30w
sin 30°
sin-10.5 = 30°!s(sin–1)0.5*2w
(xwhen sinx= 0.5)
2-4-3
Function Calculations
*1*can be omitted. *2Input of leading zero is not necessary.
π
(90°= ––– radians = 100 grads)
2

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kLogarithmic and Exponential Functions
•Be sure to specify Comp for Mode in the SET UP screen.
Example Operation
log 1.23 (log101.23) = 8.990511144 ×10–2 l1.23w
In 90 (loge90) = 4.49980967 I90w
101.23 = 16.98243652
(To obtain the antilogarithm of common !l(10x)1.23w
logarithm 1.23)
e4.5 = 90.0171313
(To obtain the antilogarithmof natural !I(ex)4.5w
logarithm 4.5)
(–3)4= (–3) ×(– 3) ×(–3) ×(–3) = 81 (-3)M4w
–34= –(3 ×3 ×3 ×3) = –81 -3M4w
1
7(= 123 7) = 1.988647795 7!M(x)123w
2 + 3 ×3– 4 = 10 2+3*3!M(x)64-4w*1
2-4-4
Function Calculations
123
64
*1^ (xy) and xtake precedence over
multiplication and division.