Rockwell Automation 1769-IF16V Compact High Density Analog Input Modules - Manual (Page 74)

74 Publication 1769-UM018A-EN-P - October 2008
Appendix D 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, 32,768, from
the sum of the values of the other positions. In all positions are 1 and
the value is 32,767 - 32,768 = -1.
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.