Rockwell Automation 1769-OF4VI Compact I/O Isolated Analog Modules - Manual (Page 118)

Publication 1769-UM014B-EN-P - May 2010
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.