Computer Hardware User's Guide

Floating-Point Multiplication
5-29 Data Formats and Floating-Point Operation
Example 5–8 through Example 5–12 illustrate how floating-point multiplication
is performed on the ’C3x. For these examples, the implied most significant
nonsign bit is made explicit.
Example 5–8. Floating-Point Multiply (Both Mantissas = –2.0)
Let:
α = –2.0 × 2
α( exp )
= 10.00000000000000000000000 × 2
α( exp )
b = –2.0 × 2
b ( exp )
= 10.00000000000000000000000 × 2
b ( exp )
Where:
α and b are both represented in binary form according to the normalized
single-precision floating-point format.
Then:
10.00000000000000000000000 × 2
α( exp )
× 10.00000000000000000000000 × 2
b ( exp )
0100.000000000000000000000000000000000000000000000 × 2
(α( exp ) +
b
( exp ))
To place this number in the proper normalized format, it is necessary to shift
the mantissa two places to the right and add 2 to the exponent. This yields:
10.00000000000000000000000 × 2
α( exp )
× 10.00000000000000000000000 × 2
b ( exp )
0100.0000000000000000000000000000000000000000000000 × 2
(α( exp ) + b ( exp ))
In floating-point multiplication, the exponent of the result may overflow. This can
occur when the exponents are initially added or when the exponent is modified
during normalization.