Computer Hardware User's Guide

Floating-Point Formats
5-12
5.3.6 Conversion Between Floating-Point Formats
Floating-point operations assume several different formats for inputs and out-
puts. These formats often require conversion from one floating-point format to
another (for example, short floating-point format to extended-precision floating-
point format). Format conversions occur automatically in hardware, with no
overhead, as a part of the floating-point operations. Examples of the four con-
versions are shown in Figure 5–10 through Figure 5–13. When a floating-point
format 0 is converted to a greater-precision format, it is always converted to a
valid representation of 0 in that format. In Figure 5–10 through Figure 5–13,
s = sign bit of the exponent, y = short mantissa, and x = short exponent.
Figure 5–10. Converting from Short Floating-Point Format to Single-Precision
Floating-Point Format
Short floating-point format
Single-precision floating-point format
yy00yxss
yy yxxs
15 12 11 10 0
31 27 24 23 22 12 11 0
x
sss xx
In this format, the exponent field is sign extended, and the 12 LSBs of the mantissa
field are filled with 0s.
Figure 5–11. Converting from Short Floating-Point Format to Extended-Precision
Floating-Point Format
Short floating-point format
Extended-precision floating-point format
y0 0
yy y
15 12 11 10 0
39 35
32 3031 20 19 0
ss
xxsx
sss yyxxx
The exponent field in this format is sign extended, and the 20 LSBs of the mantissa
field are filled with 0s.