Texas Instruments TMS320C3x User Manual
Page 120
Floating-Point Conversion (IEEE Std. 754)
5-15
Data Formats and Floating-Point Operation
Figure 5–15. TMS320C3x Single-Precision 2s-Complement Floating-Point Format
e
f
31
23
22
0
24
s
Note:
Same format as for the ’C4x
In comparison, Figure 5–15 shows the the ‘C3x 2s-complement floating-point
format. In this format, two cases can be used to define value
v of a number:
1)
If
e = –128
then
v = 0
2)
If
e
≠
–128
then
v = ss.f
2
2
e
where:
s = sign bit
e = the exponent field
f = the fraction field
For this representation,
e is treated as a 2s-complement integer. The fraction
and sign bit form a normalized 2s-complement mantissa.
Note:
Differentiating Symbols for IEEE and TMS320C3x Formats
To differentiate between the symbols that define these two formats, all IEEE
fields are subscripted with an IEEE (for example,
e
IEEE
,
s
IEEE
, and so forth).
Similarly, all 2s-complement fields are subscripted with 2 (that is,
e
2
,
s
2
,
f
2
).
5.4.1
Converting IEEE Format to 2s-Complement TMS320C3x Floating-Point Format
The most common conversion is the IEEE-to-2s-complement format. This
conversion is done according to rules in Table 5–1.
Table 5–1. Converting IEEE Format to 2s-Complement Floating-Point Format
If these values are present
Then these values equal
Description
Case
e
IEEE
s
IEEE
f
IEEE
e
2
s
2
f
2
max neg
1
1
255
1
any
7Fh
1
00 0000h
max pos
1
2
255
0
any
7Fh
0
7F FFFFh
3
0 < e
IEEE
< 255
0
f
IEEE
e
IEEE
– 7Fh
0
f
IEEE
4
0 < e
IEEE
< 255
1
≠
0
e
IEEE
– 7Fh
1
f
IEEE
+ 1
†
5
0 < e
IEEE
<255
1
0
e
IEEE
– 80h
1
0
zero
6
0
any
any
80h
0
00 0000h
† f IEEE = 1s complement of fIEEE