Texas Instruments TMS320C3x - Manual (Page 134)

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)
Ч
10.00000000000000000000000
Ч
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)
Ч
10.00000000000000000000000
Ч
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.