Interpreting Data; Table 3-2 Interpretation Of 16-Bit Data Values; Table 3-3 Interpretation Of 36-Bit Data Values - Motorola DSP56800 Manual

Data Arithmetic Logic Unit
• Conversion to floating-point representation is easier because the industry-standard floating-point
formats use fractional mantissas.
• Coefficients for most digital filters are derived as fractions by DSP digital-filter design software
packages. The results from the DSP design tools can be used without the extensive data conversions
that other formats require.
• A significant bit is not lost through sign extension.
3.3.1

Interpreting Data

Data in a memory location or register can be interpreted as fractional or integer, depending on the needs of
a user's program. Table 3-2 shows how a 16-bit value can be interpreted as either a fractional or integer
value, depending on the location of the binary point.
Binary
Representation
0.100 0000 0000 0000
0.010 0000 0000 0000
0.001 0000 0000 0000
0.111 0000 0000 0000
0.000 0000 0000 0000
1.100 0000 0000 0000
1.110 0000 0000 0000
1.111 0000 0000 0000
1.001 0000 0000 0000
1.This corresponds to the location of the binary point when the data is interpreted as fractional. If
the data is interpreted as integer, the binary point is located immediately to the right of the LSB.
The following equation shows the relationship between a 16-bit integer and a fractional value:
Fractional Value = Integer Value / (2
There is a similar equation relating 36-bit integers and fractional values:
Fractional Value = Integer Value / (2
Table 3-3 shows how a 36-bit value can be interpreted as either an integer or a fractional value, depending
on the location of the binary point.
Hexadecimal
Representation
$7 FFFF FFFF
$1 4000 0000
$0 4000 0000
$0 2000 0000
$0 0000 0000
$F C000 0000
3-16
Table 3-2. Interpretation of 16-Bit Data Values
Hexadecimal
1
Representation
$4000
$2000
$1000
$7000
$0000
$C000
$E000
$F000
$9000
15
)
31
)
Table 3-3. Interpretation of 36-bit Data Values
36-Bit Integer in
Entire Accumulator
1
(decimal)
34,359,738,367
5,368,709,120
1,073,741,824
536,870,912
0
- 1,073,741,824
DSP56800 Family Manual
Integer Value Fractional Value
(decimal)
16,384
8,192
4,096
28,672
0
- 16,384
- 8,192
- 4,096
- 28,672
16-Bit Integer in MSP
(decimal)
-
-
16,384
8,192
0
- 16,384
(decimal)
0.5
0.25
0.125
0.875
0.0
- 0.5
- 0.25
- 0.125
- 0.875
Fractional
Value
(decimal)
~ 16.0
2.5
0.5
0.25
0.0
- 0.5