3. Instructions
516
CS/CJ/NSJ Series Instructions Reference Manual (W474)
• Special Numbers
The formats for NaN, ±∞, and 0 are as follows:
• NaN*:e = 2,047 and f ≠0
•+∞:e = 2,047, f = 0, and s= 0
•-∞: e = 2,047, f = 0, and s= 1
• 0: e = 0 and f = 0
* NaN (not a number) is not a valid floating-point number. Executing Double-precision Floating-point instructions
will not result in NaN.
îš„ Writing Floating-point Data
When double-precision floating-point is specified for the data format in the I/O memory edit display in
the CX-Programmer, standard decimal numbers input in the display are automatically converted to the
double-precision floating-point format shown above (IEEE754-format) and written to I/O Memory. Data
written in the IEEE754-format is automatically converted to standard decimal format when monitored
on the display.
It is not necessary for the user to be aware of the IEEE754 data format when reading and writing
double-precision floating-point data. It is only necessary to remember that double-precision floating
point values occupy four words each.
îš„ 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 significant digits. If the result of calculations is a non-normalized number (including
intermediate results), the number of significant digits will be reduced.
(1) 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 2,046, and the real exponent will be 1,023 less, i.e., -
1,022 to 1,023.
The mantissa (f) will be expressed from 0 to (2
52
- 1), and it is assumed that, in the real mantissa,
bit 2
52
is 1 and the decimal point follows immediately after it.
Normalized numbers are expressed as follows:
(-1)
(sign s)
× 2
(exponent e)-1,023
× (1 + mantissa × 2
-52
)
Example
Mantissa (f)
Exponent (e)
0 Not 0 and not all 1's (1,024) All 1's (1,024)
0 0 Normalized number Infinity
Not 0 Non-normalized number NaN
0
6362 5251 161532314847
f
n
se
n+3 n+2 n+1
00000000000000000000000000000000
11000000000011000000000000000000
63 62 52 51
33
32
0
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