Allen-Bradley MicroLogix 1200, User Manual, Page: 100 / 144

Publication 1762-UM002A-EN-P - July 2002
B-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 the figure below (all
positions are 1), the value is 32767 - 32768 = -1. For 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.