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) × 2127 = 3.4028234 ×1038
Least positive:
x
= 1 × 2–127 = 5.8774717541 × 1038
Least negative:
x
= (–1–2–31) × 2–127 = – 5.8774717569 ×10–39
Most negative:
x
= –2 × 2127 = – 3.4028236691 ×1038
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
= 101000000002, then
man
= 01.101000000002:
s Fraction
010100000000
Rewrite the mantissa as:
Mantissa
01.1 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
= 101000000002,
then
man
= 10.101000000002.
s Fraction
110100000000