Rockwell Automation 1769-IR6 Compact I/O 1769-IR6 RTD/Resistance Input Module - Manual (Page 110)

110 Rockwell Automation Publication 1769-UM005B-EN-P - March 2012
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, 32768, from the sum of the values
of the other positions. In the figure below (all positions are 1), the value is
32767 - 32768 = -1. For 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.