dsp56800 Freescale Semiconductor, Inc, dsp56800 Datasheet - Page 60

• Manufacturer Part Number: dsp56800
• Description: 16-bit Digital Signal Controllers
• Manufacturer: Freescale Semiconductor, Inc

Data Arithmetic Logic Unit
3.3.1
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.
The following equation shows the relationship between a 16-bit integer and a fractional value:
There is a similar equation relating 36-bit integers and fractional values:
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.
3-16
•
•
•
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 DSC digital-filter design software
packages. The results from the DSC design tools can be used without the extensive data conversions
that other formats require.
A significant bit is not lost through sign extension.
Fractional Value = Integer Value / (2
Fractional Value = Integer Value / (2
Interpreting Data
Representation
Hexadecimal
Representation
$7 FFFF FFFF
$F C000 0000
Hexadecimal
$1 4000 0000
$0 4000 0000
$0 2000 0000
$0 0000 0000
$7FFF
$E000
$C000
$7000
$4000
$2000
$1000
$0000
$F000
$9000
$8000
1
0111 1111 1111 1111.
0111 0000 0000 0000.
0100 0000 0000 0000.
0010 0000 0000 0000.
0001 0000 0000 0000.
0000 0000 0000 0000.
1111 0000 0000 0000.
1110 0000 0000 0000.
1100 0000 0000 0000.
1001 0000 0000 0000.
1000 0000 0000 0000.
Table 3-2. Interpretation of 16-Bit Data Values
Table 3-3. Interpretation of 36-bit Data Values
Binary
Entire Accumulator
36-Bit Integer in
- 1,073,741,824
34,359,738,367
Integer
5,368,709,120
1,073,741,824
DSP56800 Family Manual
536,870,912
(decimal)
15
31
0
)
)
Decimal
- 16384
- 28672
- 32768
32767
28672
16384
- 4096
- 8192
8,192
4,096
0
16-Bit Integer in MSP
0.111 1111 1111 1111
0.111 0000 0000 0000
0.100 0000 0000 0000
0.010 0000 0000 0000
0.001 0000 0000 0000
0.000 0000 0000 0000
1.111 0000 0000 0000
1.110 0000 0000 0000
1.100 0000 0000 0000
1.001 0000 0000 0000
1.000 0000 0000 0000
(Overflows)
(Overflows)
(decimal)
- 16,384
16,384
8,192
Binary
0
Fractional
Freescale Semiconductor
Fractional
(decimal)
Decimal
0.99997
- 0.125
- 0.875
~ 16.0
Value
- 0.25
0.875
0.125
0.25
- 0.5
- 0.5
- 1.0
0.25
2.5
0.5
0.0
0.5
0.0