Computer Hardware User's Guide
Floating-Point Formats
5-6
The following examples illustrate the range and precision of the short floating-
point format:
Most positive:
x
= (2 – 2
–11
) × 2
7
= 2.5594 × 10
2
Least positive:
x
= 1 × 2
–7
= 7.8125 × 10
–3
Least negative:
x
= (–1–2
–11
) × 2
–7
= –7.8163 × 10
–3
Most negative:
x
= –2 × 2
7
= –2.5600 × 10
2
5.3.2 TMS320C32 Short Floating-Point Format for External 16-Bit Data
To facilitate the handling of 16-bit floating-point data types, the ‘C32 uses a new
short floating-point format for external 16-bit data types. Note that the following
short floating-point format is used only in external 16-bit floating-point data
access. This format is different than the 16-bit immediate short floating-point
data format used in the ‘C32’s instruction set.
In the short floating-point format for external 16-bit data-type size, floating-point
numbers are represented by a 2s-complement, 8-bit exponent field (
e
), a sign bit
(
s
), and an 8-bit mantissa field (
man
) with an implied most significant nonsign bit.
Figure 5–7. TMS320C32 Short Floating-Point Format for External 16-Bit Data
Exponent Sign Fraction
15 0876
Mantissa
Operations are performed with an implied binary point between bits 7 and 6.
When the implied most significant nonsign bit is made explicit, it is located to the
immediate left of the binary point. The floating-point 2s-complement number
x
in the short floating-point format is given by:
x
= 01.f × 2
e
if
s
= 0
x
= 10.f × 2
e
if
s
= 1
x
= 0 if
e
= –128
You must use the following reserved values to represent 0 in the ‘C32 short
floating-point format for external 16-bit data:
e
= –128
s
=0
f
=0