Lecture Notes for Computer Architecture II - St. Cloud State University

Normalized Form keeps one digit left to the binary point
For example
1.000111
This can be written as
n
(1 + F) 2
Fraction - F
Exponent - n
Page | 107
In the IEEE standard we have to add 127 to the exponent in single precision
In the IEEE standard we have to add 1023 to the exponent in double precision
– SP (127)
DP (1023)
Compromise
Accuracy
Fraction
Range
Exponent
Example
.75 10
.11000 binary
.75 X 2 = 1.50
.5 X 2 = 1.0
.75 10 = .11 2
Normalized form
0.11 = 1.1 2 -1
IEEE standard format single precision
0 126 10000000000000
-1 + 127 23 bit
Another Example .9 10
.9 * 2 = 1.8
.8 * 2 = 1.6
.6 * 2 = 1.2
.2 *2 = 0.4
.4 * 2 = 0.8
.9 = .11100