Texas Instruments TMS320C3x User Manual
Page 135
Floating-Point Multiplication
5-30
Example 5–9. Floating-Point Multiply (Both Mantissas = 1.5)
Let:
α
= 1.5
×
2
α
(
exp)
= 01.0000000000000000000000
×
2
α
(
exp)
b
= 1.5
×
2
b(exp)
= 01.0000000000000000000000
×
2
b(exp)
Where:
a and b are both represented in binary form according to the single-preci-
sion floating-point format.
Then:
10.00000000000000000000000
×
2
α
(
exp)
x 10.00000000000000000000000
×
2
b(exp)
01.0000000000000000000000000000000000000000000000
×
2
(
α
(
exp) + b(exp) + 2)
To place this number in the proper normalized format, it is necessary to shift
the mantissa one place to the right and add 1 to the exponent. This yields:
01.0000000000000000000000
×
2
α
(
exp)
Ч
01.0000000000000000000000
Ч
2
b(exp)
01. 00100000000000000000000000000000000000000000000
×
2
(
α
(
exp) + b(exp) + 1)
Example 5–10. Floating-Point Multiply (Both Mantissas = 1.0)
Let:
α
= 1.0
×
2
α
(
exp)
= 01.00000000000000000000000
×
2
α
(
exp)
b
= 1.0
×
2
b(exp)
= 01.00000000000000000000000
×
2
b(exp)
Where:
a and b are both represented in binary form according to the single-preci-
sion floating-point format.
Then:
01.00000000000000000000000
×
2
α
(
exp)
Ч
01.00000000000000000000000
Ч
2
b(exp)
0001.0000000000000000000000000000000000000000000000 y 2
(
a(exp) + b(exp))
This number is in the proper normalized format. Therefore, no shift of the
mantissa or modification of the exponent is necessary.
The previous examples show cases where the product of two normalized
numbers can be normalized with a shift of 0, 1, or 2. The floating-point format
of the ‘C3x makes this possible.