Omron CJ1G-CPUxx, Instructions Manual

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Floating-point Math Instructions
Section 3-15
Numbers Expressed as Floating-point Values
The following types of floating-point numbers can be used.
Note A non-normalized number is one whose absolute value is too small to be
expressed as a normalized number. Non-normalized numbers have fewer sig-
nificant digits. If the result of calculations is a non-normalized number (includ-
ing intermediate results), the number of significant digits will be reduced.
Normalized Numbers Normalized numbers express real numbers. The sign bit will be 0 for a positive
number and 1 for a negative number.
The exponent (e) will be expressed from 1 to 254, and the real exponent will
be 127 less, i.e., –126 to 127.
The mantissa (f) will be expressed from 0 to 2
33
– 1, and it is assume that, in
the real mantissa, bit 2
33
is 1 and the binary point follows immediately after it.
Normalized numbers are expressed as follows:
(–1)
(sign s)
x 2
(exponent e)–127
x (1 + mantissa x 2
–23
)
Example
Sign: –
Exponent: 128 – 127 = 1
Mantissa: 1 + (2
22
+ 2
21
) x 2
–23
= 1 + (2
–1
+ 2
–2
) = 1 + 0.75 = 1.75
Value: –1.75 x 2
1
= –3.5
Non-normalized Numbers Non-normalized numbers express real numbers with very small absolute val-
ues. The sign bit will be 0 for a positive number and 1 for a negative number.
The exponent (e) will be 0, and the real exponent will be –126.
The mantissa (f) will be expressed from 1 to 2
33
– 1, and it is assume that, in
the real mantissa, bit 2
33
is 0 and the binary point follows immediately after it.
Non-normalized numbers are expressed as follows:
(–1)
(sign s)
x 2
–126
x (mantissa x 2
–23
)
Example
Sign: –
Exponent: –126
Mantissa: 0 + (2
22
+ 2
21
) x 2
–23
= 0 + (2
–1
+ 2
–2
) = 0 + 0.75 = 0.75
Value: –0.75 x 2
–126
Zero Values of +0.0 and –0.0 can be expressed by setting the sign to 0 for positive
or 1 for negative. The exponent and mantissa will both be 0. Both +0.0 and
–0.0 are equivalent to 0.0. Refer to Floating-point Arithmetic Results, below,
for differences produced by the sign of 0.0.
Infinity Values of +
∞
and –
∞
can be expressed by setting the sign to 0 for positive or 1
for negative. The exponent will be 255 (2
8
– 1) and the mantissa will be 0.
Mantissa (f) Exponent (e)
0 Not 0 and
not all 1’s All 1’s (255)
0 0 Normalized number Infinity
Not 0 Non-normalized
number NaN
1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 30 23 22 0
0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 30 23 22 0