Rockwell Automation 1769-IT6 Compact I/O 1769-IT6 Thermocouple/mV Input Module - Manual (Page 112)

112 Rockwell Automation Publication 1769-UM004B-EN-P - March 2010
Appendix B 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. In the figure below (all positions are 1), the value is 32,767
- 32,768 = -1. This is an example.
1111 1000 0010 0011 = (214+213+212+211+25+21+20) - 215 =
(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.