8
Number Systems
Because a PLC is a computer, it stores information in the form
of on or off conditions (1 or 0), referred to as
bits. Sometimes
bits are used individually and sometimes they are used
to represent numerical values. Understanding how these
bits can be used to represent numerical values requires an
understanding of the
binary number system.
Decimal System In order to understand the binary number system, it is
first useful to recall some of the basics of the
decimal
number system. All number systems have the same three
characteristics: digits, base, weight. For example, the decimal
system has the following characteristics:
Ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Base 10
Weights Powers of base 10 (1, 10, 100, 1000, ...)
Binary System The binary system has the following characteristics:
Two digits: 0, 1
Base 2
Weights Powers of base 2 (1, 2, 4, 8, 16, ...)
The binary system has a base of 2 and uses only two
characters, 1 and 0. Each bit is associated with a power of 2
based on its position in the number. The further to the left,
the higher the power of 2. The number in the far left-hand
column is referred to as the
most significant bit or MSB and
the number in the far right-hand column is referred to as the
least significant bit or LSB. A 1 is placed in a position if that
power of 2 is used in the number. Otherwise, a 0 is placed in a
position.
128 64 32 16 8 4
2 1
0 0 0
1 1
0 0 0
Most Significant Bit (MSB)
Least Significant Bit (LSB)
2
7
2
6
2
5
2
4
2
3
2
2
2
1
2
0
00011000 in binary = 24 in Decimal
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