Rockwell Automation 1772-LP3 PLC - 2/30 Programmable Controller Programming and Operations Manual - Manual (Page 327)

Number Systems
Appendix B
BĆ3
The binary numbering system uses a number set that consists of two
digits: the numbers 0 and 1. All information in memory is stored as an
arrangement of 1 and 0.
Each digit in a binary number has a certain place value expressed as a
power of two (Figure B.3). The decimal equivalent of a binary number is
computed by multiplying each binary digit by its corresponding place
value and adding these numbers together.
By grouping several binary digits together, values can be formed to
represent decimal or octal numbers.
Figure B.3
Binary Numbering System
1 x 2 7 = 128
1 x 2 6 = 64
1 x 2 5 = 32
0 x 2 4 = 0
1 x 2 3 = 8
1 x 2 2 = 4
1 x 2 1 = 2
1 x 2 0 = 1
1 1 1 0 1 1 1 1
128
64
32
8
4
2
1
239
10
11101111
2
= 239
10 2
B.3
Binary Numbering System