Computer Hardware User's Guide

Floating-Point Formats
5-9 Data Formats and Floating-Point Operation
The following examples illustrate the range and precision of the extended-
precision floating-point format:
Most positive:
x = (2 – 2
–23
) × 2
127
= 3.4028234 × 10
38
Least positive: x = 1 × 2
–127
= 5.8774717541 × 10
38
Least negative: x = (–1–2
–31
) × 2
–127
= – 5.8774717569 × 10
–39
Most negative: x = –2 × 2
127
= – 3.4028236691 × 10
38
5.3.5 Determining the Decimal Equivalent of a TMS320C3x Floating-Point Format
To convert a ‘C3x floating-point number to its decimal equivalent, follow these
steps:
Step 1: Convert the exponent field to its decimal representation.
The exponent field is a 2s-complement number. To convert a 2s-
complement number, look at the MSB. If it is 0, then convert the
binary number to a decimal number. If the MSB is 1, then comple-
ment the binary number, add 1 to the result, and then convert this
binary number to a decimal number.
Step 2: Convert the mantissa field to its decimal representation.
The mantissa field is represented as a sign-mantissa number with an
implied 1 and an implied binary point between the sign bit and the frac-
tion field. If the sign bit is cleared (
s = 0), form the mantissa by writing
01, and appending the bits in the fraction field after the binary point.
For example, if f = 10100000000
2
, then man = 01.10100000000
2
:
s Fraction
0
1 0 1 0 0 0 0 0 0 0 0
Rewrite the mantissa as:
Mantissa
0
1
.
1 0 1 0 0 0 0 0 0 0 0
If the sign bit is set ( s = 1), form the mantissa by writing 10 and appending the
bits in the fraction field after the binary point. For example, if f = 10100000000
2
,
then man = 10.10100000000
2
.
s Fraction
1
1 0 1 0 0 0 0 0 0 0 0