Solartron Mobrey 3595 4C, User Manual

Page: 112 / 128

Results and Error Formats 3595 4C User Manual Part Two
2-4
35952350 (CH02/AA)
2.2 IEEE 754 FLOATING-POINT NUMBER FORMAT
The IEEE 754 floating-point number format is used for the ‘event totalise’ and ‘event increment’ results, as
returned by the 3595 IMP types 2A and 2B. It is also used for the response to the IN command, and for the
set-up parameters in several IMP commands.
To represent a number in IEEE 754 format, four bytes are used:
S e
7
...... e
1
First Byte
m
22
..... m
16
e
0
m
15
..... m
8
m
7
..... m
0
Fourth Byte
Sign bit (most significant bit of first byte)
Binary exponent with excess of 127
(e
7
= most significant)
Implied 1. of mantissa
Fractional part of mantissa
(m
22
= most significant)
The S (sign) bit is one if the number is negative and zero if the number is positive. The binary exponent has
an excess of 127
10
. This means that it consists of the sum of the true exponent with 127
10
. This allows a
range of exponent values from -127
10
to 128
10
. To retrieve the true exponent, subtract 127
10
. The mantissa
has an ‘implied one’. Only the fractional part of the mantissa is actually written. When the number is
converted to IEEE format, the exponent is adjusted until there is only a single binary one to the left the
binary zero. This binary one is then omitted and becomes ‘implied’.
Example: To convert a decimal number of 2.25
2.25
10
= 10.01
2
= 10.01 * 2
0
= 1.001 * 2
1
Mantissa (with implied 1) = .001
Exponent = 1
with excess of 127 = 127+1 = 128
This gives the result:
0 1000000 0 0010000 00000000 00000000
The result breaks down into:
Sign bit = 0, therefore the number is positive.
An exponent with the excess of 127
10
= 10000000
2
= 128
10
, the true binary exponent is 1
10
.
Mantissa with implied 1 = 001…., a true mantissa of 1.001
2
.
The four bytes there represent:
1.001
2
* 2
1
= 10.01
2
= 2.25
10
Note: Zero is represented by all four bytes being ‘all zeroes’.