Rockwell Automation Allen-Bradley 1769-IF4, User Manual

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Publication 1769-UM002B-EN-P - July 2005
E-2 Two’s Complement Binary Numbers
Negative Decimal Values
In two’s complement notation, the far left position is always 1 for negative
values. The equivalent decimal value of the binary number is obtained by
subtracting the value of the far left position, 32768, from the sum of the values
of the other positions. In Figure E.2 all positions are 1 and the value is 32767 -
32768 = -1.
Figure E.2 Negative Decimal Values
EXAMPLE
1111 1000 0010 0011 = (2
14+
2
13+
2
12+
2
11+
2
5+
2
1+
2
0
) - 2
15
=
(16384+8192+4096+2048+32+2+1) - 32768 =
30755 - 32768 = -2013
1 x 2 = 2
1 x 2 = 1
1 x 2 = 16384
1 x 2 = 8192
1 x 2 = 4096
1 x 2 = 2048
1 x 2 = 1024
1 x 2 = 128
1 x 2 = 512
1 x 2 = 256
1 x 2 = 64
1 x 2 = 32
1 x 2 = 16
1 x 2 = 8
1 x 2 = 4
1 x 2 = 32768
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
14
13
12
11
10
9
8
7
6
5
4
3
2
1
15
0
16384
8192
4096
2048
1024
512
256
128
64
32
16
8
4
2
1
32767
This position is always 1 for negative numbers.