Siemens 500 NIM - Manual (Page 127)

Floating Point Numbers B-5 SIMATIC TIWAY I Series 500 NIM User Manual
B.3 IEEE Format
The exponent portion of the IEEE format is similar to the IBM format
except that it is 8 bits in length and is biased by 7F
16. It is also different in
that it represents a power of 2 instead of 16. The exponent for 2
) is
represented in memory by 7F
16. Negative exponents are represented by
numbers less than 7F 16. For example, a 2–! is represented in the
exponent field by by a value of 7E 16. The exponents may be any value from
–7E 16 to +7F16 (2–!@^ to 2!@&). The eight exponent bits are stored in
bits 1 – 8 of the first memory word. See Figure B-2.
The fraction portion of the IEEE format is similar to the IBM format. It is a
hexadecimal fraction which is interpreted in one of many ways, depending
on the value of the exponent. Table B-1 describes the different types of
conversions for the IEEE format.
Table B-1 IEEE Conversions
Case
A
B
C
D
E
Exponent
FF
FF
00 < e < FF
00
00
16
16
16
16
16 16
Fraction
non-zero
0
any value
non-zero
0
v (IEEE) = decimal value
NaN (regardless of sign bit)
+/-
(-1) * 2 *(1.f)
(-1) * 2 *(0.f)
+/-0 (depending on sign bit)
s
s (e-127)
-126
Note: s = sign bit; f = fraction; e = exponent
1
Case A is an illegal value. A Not-a-Number (NaN) will never be returned
from the Series 500 NIM. If this example is written to the NIM, an
exception will be returned.
Case B, +/– infinity, is used to represent numbers too large in magnitude to
be represented with the IEEE format.
Case C represents a normalized IEEE floating point value. (There is a one,
not included in f, to the left of the radix point.)
Case D represents a denormalized IEEE floating point (contains a zero to
the left of the radix point).
Case E represents a value of zero. Numbers too small to be represented in
the IEEE format will be reported as a positive or a negative 0.