Rockwell Automation 1746-NI16V SLC 500 Analog Input Modules User Manual - Manual (Page 108)

Publication 1746-UM001A-US-P
C-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, 32,768, from
the sum of the values of the other positions. In the figure below (all
positions are 1), the value is 32,767 - 32,768 = -1. For example:
1111 1000 0010 0011 =
(2
14
+2
13
+2
12
+2
11
+2
5
+2
1
+2
0
) - 21
5
=
(16384+8192+4096+2048+32+2+1) - 32,768 =
30,755 - 32,768 = -2013.
1x2 14 = 16384
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
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1x2 15 = 32,768 This position is always 1 for negative numbers.
16384
8192
4096
2048
1024
512
256
128
64
32
16
8
4
2
1
32767