Rockwell Automation 1746-FIO4V SLC 500 Fast Analog I/O/ User Manual - Manual (Page 85)

Publication 1746-UM009B-EN-P - September 2007
2’s-complement Binary Numbers 85
Negative Decimal Values
The far left position is always 1 for negative values. The equivalent
decimal value of a negative 2’s-complement binary number is
obtained by subtracting 32768 from the sum of the other position
values. In the figure below, all positions are 1 and the value is 32767 –
32768 = –1. Study this 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
This position is always 1 for negative numbers (1x2
15
= 32,768)
1x2
14
=16,384
1x2
13
= 8192
1x2 12 = 4096
1x2
11
= 2048
1x2
10
= 1024
1x2
9
= 512
1x2 8 = 256
1x2
7
= 128
1x2
6
= 64
1x2
5
= 32
1x2 4 = 16
1x2
3
= 8
1x2
2
= 4
1x2 1 = 2
1x2
0
= 1
1
2
4
8
16
32
64
128
256
512
1024
2048
4096
8192
16,384
32,767 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1S 1