Data Formats; Signed Fractional; Unsigned Fractional - Motorola DSP56800 Manual

Table 3-3. Interpretation of 36-bit Data Values (Continued)
Hexadecimal
Representation
$F E000 0000
$E C000 0000
$8 0000 0001
When the accumulator extension registers are in use, the data contained in the accu-
1.
mulators cannot be stored exactly in memory or other registers. In these cases the data
must be limited to the most positive or most negative number consistent with the size
of the destination.
3.3.2

Data Formats

Four types of two's-complement data formats are supported by the 16-bit DSP core:
•

Signed fractional

•

Unsigned fractional

• Signed integer
• Unsigned integer
The ranges for each of these formats, discussed in the following subsections, apply to all data stored in
memory and to data stored in the data ALU registers. The extension registers associated with the
accumulators allow word growth so that the most positive signed fractional number that can be represented
in an accumulator is approximately 16.0 and the most negative signed fractional number is -16.0 as shown
in Table 3-3. An important factor to consider is that when the accumulator extension registers are in use,
the data contained in the accumulators cannot be stored exactly in memory or other registers. In these cases
the data must be limited to the most positive or most negative number consistent with the size of the
destination and the sign of the accumulator, the MSB of the extension register.
3.3.2.1 Signed Fractional
In this format the N bit operand is represented using the 1.[N-1] format (1 sign bit, N-1 fractional bits).
Signed fractional numbers lie in the following range:
-1.0 ≤ SF ≤ +1.0 - 2
For words and long-word signed fractions, the most negative number that can be represented is -1.0, whose
internal representation is $8000 and $80000000, respectively. The most positive word is $7FFF or 1.0 -
-15
2 , and the most positive long word is $7FFFFFFF or 1.0 - 2
3.3.2.2 Unsigned Fractional
Unsigned fractional numbers may be thought of as positive only. The unsigned numbers have nearly twice
the magnitude of a signed number with the same number of bits. Unsigned fractional numbers lie in the
following range:
0.0 ≤ UF ≤ 2.0 - 2
Examples of unsigned fractional numbers are 0.25, 1.25, and 1.999. The binary word is interpreted as
having a binary point after the MSB. The most positive 16-bit unsigned number is $FFFF or {1.0 + (1.0 - 2
- [N-1]
)} = 1.99996948. The smallest unsigned number is zero ($0000).
36-Bit Integer in
Entire Accumulator
1
(decimal)
- 536,870,912
- 5,368,709,120
-34,359,738,367
-[N-1]
-[N-1]
Data Arithmetic Logic Unit
Fractional and Integer Data ALU Arithmetic
16-Bit Integer in MSP
(decimal)
- 8,192
-
-
-31
.
Fractional
Value
(decimal)
- 0.25
-2 .5
-16.0
3-17