Rockwell Automation 1772-L8_LW_LWP_LX_LXP,D17726.5.8 User Manual User Manual
Page 416
Number Systems
Appendix C
C-3
Binary numbering is used in all digital systems to store and manipulate
data. This is a numbering system made up of two numbers: 0 and 1
(Table C.A). All binary numbers are composed of these digits.
Information in memory is stored as an arrangement of 1 and 0. The value
of binary number depends on the digits used and the place value of
each digit.
Each place value in a binary number represents a power of two starting
with two raised to the zero power (2
0
=1) (Figure C.3). You can compute
the decimal value of a binary number by multiplying each binary digit by
its corresponding place value and adding these numbers together.
Figure C.3
Binary Numbering System
1
1
1
1
1
1
1
0
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
128
64
32
8
4
2
1___
239
10
11101111
2
= 239
10
10406-I
Binary Coded Decimal System
The binary coded decimal (BCD) format expresses a decimal value as an
arrangement of binary digits. Each group of 4 binary digits is used to
represent a decimal number from 0 to 9. All BCD numbers are composed
of these digits. The value of BCD number depends on the digits used and
the place value of these digits.
Each place value in a BCD number represents a power of two starting with
two raised to the zero power (2
0
=1) (Figure C.4). You can compute the
decimal value of a binary number by multiplying each binary digit by its
corresponding place value and adding these numbers together.
Binary Numbering System