Sharp OZ-707 Operation Manual - Page 20

Priority in Direct Input Calculations, Printing for Direct Input Calculations, Calculation Errors

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Priority in Direct Input Calculations You can enter formulas in the exact order in which they are written, including parentheses or functions. The order of priority in calculation and treatment of intermediate results will be taken care of by the Card. The internal order of priority in manual calculation is as follows: 1. Recalling variables or PI . 2. Function (sin, cos, etc.) 3. Power (A), root (ROT) 4. Sign (+, -) 5. Multiplication or division (*, / ) 6. Addition or subtraction (+, -) 7 . Comparison of magnitude 8. Logical AND, OR, XOR Note: • If parentheses are used in a formula, the operation given within the parentheses has the highest priority. 1 • Composite function,s are operated from right to left (sin cos- 0.6). • Chained power (34 or 3 A 4 A 2) is operated from right to left. • For items 3) and 4) above, the last entry has higher priority. (e.g.) -2 A 4 -7 -(24) 3 A -2 -73-2 Printing for Direct Input Calculations The calculation steps and results can be printed if the optional printer is connected and switched on, and the I SHIFT II ENTER I keys are pressed (Print mode). If a printout is not desired, either switch off the printer, or press ISHIFT I I ENTER I again (Non-Print mode). 28 Calculation Errors The following types of errors occur in ordinary calculators, pocket computers, personal computers and also this Card: Errors due to Least Significant Digit Processing Usually, the maximum number of digits that can be calculated in a computer is:ixed. For example, 4/3 results in 1.33333333333· ··. In a computer wl~h ~ .maxim~~ of 8 digits, the 8 digits are significant digits; other least significant digits are either truncated or rounded. Example: Computer with 10 significant digits 10 significant digits 41 : 131 ENTER 1-7 1.33333333333.. . Truncated, rounded Therefore the calculated result differs from the true value by the amount truncated or rounded. (This difference is the error.) ~n the Card, a.1 ~-digit calcula~ed result is obtained (or a 24-digit result In double-precls.'o.n ~ode). T~ls result is rounded and specially processed to minimize error In the displayed value. Example in single-precision mode: 4/3 x 3 4 I : I 3 [K] 3 I ENTER I -7 4 Calculated in succession 4 I : I 3 [8] 3 I ENTER I ENTER I1--77 1.333333333 1 3.999999999 Calculated independently ~hen ~a.lculate~ in succession, the result of 4/3 is obtained internally In 12 digits and IS used for calculation and then rounded. When calculat~d independently, the displayed value (10 digits) is used for the calculation. Example in double-precision mode: 4/3 x 3 41: 13[8]3IENTERI-74# Calculated in succession 4 I : I3 IENTER I -7 1.3333333333333333333# } Calculated [K] 3 IENTER I -7 3.9999999999999999999# independently 29

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Priority in Direct Input Calculations
You can enter formulas in the exact order
in
which they are written,
including parentheses
or
functions. The order of priority in calculation
and treatment of intermediate results will
be
taken care of by the Card.
The internal order of priority in manual calculation is as follows:
1. Recalling variables
or
PI
.
2.
Function (sin, cos, etc.)
3. Power
(A),
root (ROT)
4. Sign
(+,
-)
5.
Multiplication
or
division
(*, / )
6. Addition or subtraction (+,
-)
7.
Comparison of magnitude
(>,
>
=,
<, <
=,
<
>,
=)
8.
Logical AND, OR, XOR
Note:
• If parentheses are used
in
a formula, the operation given within the
parentheses has the highest priority.
•
Composite functions are operated from right to left (sin cos-
1
0.6).
,
• Chained power (3
4
or
3
A
4
A
2)
is operated from right to left.
• For items 3) and
4)
above, the last entry has higher priority.
(e.g.)
-2
A
4
-7
-(24)
3
A
-2
-73-
2
Printing for Direct Input Calculations
The calculation steps and results can be printed if the optional printer
is connected and switched on, and the I
SHIFT
II
ENTER
I
keys are pressed
(Print mode).
If a printout is not desired, either switch off the printer, or press
I
SHIFT
I
I
ENTER
I
again (Non-Print mode).
28
Calculation Errors
The following types of errors occur
in
ordinary calculators, pocket
computers, personal computers and also this Card:
Errors due to Least Significant Digit Processing
Usually, the maximum number of digits that can be calculated in a
computer is:ixed. For example, 4/3 results in 1.33333333333···.
In
a
computer
wl~h
~
.maxim~~
of 8 digits, the 8 digits are significant digits;
other least significant digits are either truncated or rounded.
Example:
Computer with 10 significant digits
10 significant digits
41
:
131
ENTER
1-7 1.33333333333 .. .
Truncated, rounded
Therefore the calculated result differs from the true value by the
amount truncated
or
rounded. (This difference is the error.)
~n
the Card,
a.1
~-digit
calcula~ed
result is obtained (or a 24-digit result
In
double-precls.'o.n
~ode).
T~ls
result is rounded and specially
processed to minimize error
In
the displayed value.
Example
in
single-precision mode: 4/3
x
3
4 I :
I
3
[K]
3 I
ENTER
I
-7
4
Calculated in succession
4 I :
I
3
I
ENTER
1-7 1.3333333331
[8]
3 I
ENTER
I
-7
3.999999999
Calculated independently
~hen
~a.lculate~
in
succession, the result of 4/3 is obtained internally
In
12 digits and
IS
used for calculation and then rounded.
When
calculat~d
independently, the displayed value (10 digits) is used
for the calculation.
Example
in
double-precision mode: 4/3
x
3
41:
13[8]3IENTERI-74#
Calculated
in
succession
4 I :
I
3
I
ENTER
I
-7
1.3333333333333333333# }
Calculated
[K]
3
I
ENTER
I
-7
3.9999999999999999999#
independently
29