Rockwell Automation 1769-IF4FXOF2F Compact Combination Fast Analog I/O Module - Manual (Page 84)

84 Publication 1769-UM019A-EN-P - October 2008
Appendix D Two’s Complement Binary Numbers
Negative Decimal Values In two’s complement notation, the leftmost position is always 1 for
negative values. The equivalent decimal value of the binary number is
obtained by subtracting the value of the leftmost position, 32,768,
from the sum of the values of the other positions. 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.