Computer Hardware User's Guide

Floating-Point Addition and Subtraction
5-34
The following examples describe the floating-point addition and subtraction
operations. It is assumed that the data is in the extended-precision floating-
point format.
Example 5–13. Floating-Point Addition
In the case of two normalized numbers to be summed, let
α = 1.5 = 01.1000000000000000000000000000000 × 2
0
b = 0.5 = 01.0000000000000000000000000000000 × 2
–1
It is necessary to shift b to the right by 1 so that α and b have the same exponent.
This yields:
b = 0.5 = 00.1000000000000000000000000000000 × 2
0
Then:
01.10000000000000000000000000000000 × 2
+00.10000000000000000000000000000000 × 2
0
010.00000000000000000000000000000000 × 2
0
As in the case of multiplication, it is necessary to shift the binary point one place
to the left and add 1 to the exponent. This yields:
01.1000000000000000000000000000000 × 2
0
± 00.1000000000000000000000000000000 × 2
0
01.0000000000000000000000000000000 × 2
1