Binary Multiplication; C.4 Binary Multiplication - Analog Devices adsp-2100 Manual

The notation used to describe a format consists two numbers separated by
a period (.); the first number is the number of bits to the left of radix point,
the second is the number of bits to the right of the radix point. For
example, 16.0 format is an integer format; all bits lie to the left of the radix
point. The format in Figure C.2 is 13.3.
Table C.1 shows the ranges of numbers representable in the fractional
formats that are possible with 16 bits.
Format Number of Number of
Integer
Bits
1.15 1
2.14 2
3.13 3
4.12 4
5.11 5
6.10 6
7.9 7
8.8 8
9.7 9
10.6 10
11.5 11
12.4 12
13.3 13
14.2 14
15.1 15
16.0 16
Table C.1 Fractional Formats And Their Ranges
C.4

BINARY MULTIPLICATION

In addition and subtraction, both operands must be in the same format
(signed or unsigned, radix point in the same location) and the result
format is the same as the input format. Addition and subtraction are
performed the same way whether the inputs are signed or unsigned.
In multiplication, however, the inputs can have different formats, and the
result depends on their formats. The ADSP-2100 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
Numeric Formats
Largest Positive
Fractional Value (0x7FFF)
Bits In Decimal
15 0.999969482421875
14 1.999938964843750
13 3.999877929687500
12 7.999755859375000
11 15.999511718750000
10 31.999023437500000
9 63.998046875000000
8 127.996093750000000
7 255.992187500000000
6 511.984375000000000
5 1023.968750000000000
4 2047.937500000000000
3 4095.875000000000000
2 8191.750000000000000
1 16383.500000000000000
0 32767.000000000000000
Largest Negative Value of 1 LSB
Value (0x8000) (0x0001)
In Decimal In Decimal
–1.0 0.000030517578125
–2.0 0.000061035156250
–4.0 0.000122070312500
–8.0 0.000244140625000
–16.0 0.000488281250000
–32.0 0.000976562500000
–64.0 0.001953125000000
–128.0 0.003906250000000
–256.0 0.007812500000000
–512.0 0.015625000000000
–1024.0 0.031250000000000
–2048.0 0.062500000000000
–4096.0 0.125000000000000
–8192.0 0.250000000000000
–16384.0 0.500000000000000
–32768.0 1.000000000000000
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