Analog Devices ADSP-BF535 Blackfin, Hardware Reference Manual

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ADSP-BF535 Blackfin Processor Hardware Reference D-5
Numeric Formats
In multiplication, however, the inputs can have different formats, and the
result depends on their formats. The Blackfin family assembly language
allows you to specify whether the inputs are both signed, both unsigned,
or one of each (mixed-mode). The location of the radix point in the result
can be derived from its location in each of the inputs. This is shown in
Figure D-3 . The product of two 16-bit numbers is a 32-bit number. If the
inputs’ formats are M.N and P.Q, the product has the format
(M+P).(N+Q). For example, the product of two 13.3 numbers is a 26.6
number. The product of two 1.15 numbers is a 2.30 number.
Fractional Mode and Integer Mode
A product of 2 two’s-complement numbers has two sign bits. Since one of
these bits is redundant, you can shift the entire result left one bit. Addi-
tionally, if one of the inputs was a 1.15 number, the left shift causes the
result to have the same format as the other input (with 16 bits of addi-
tional precision). For example, multiplying a 1.15 number by a 5.11
number yields a 6.26 number. When shifted left one bit, the result is a
5.27 number, or a 5.11 number plus 16 LSBs.
Figure D-3. Format of Multiplier Result
General Rule 4-Bit Example
16-Bit Examples
M.N
x P.Q
(M+P).(N+Q)
1.111 (1.3 Format)
x 11.11 (2.2 Format)
1111
1111
1111
1111
111.00001 (3.5 Format = (1+2).(2+3))
5.3
x 5.3
10.6
1.15
x 1.15
2.30