Number Systems

Since a PLC is a computer, it stores information in the form of
On or Off conditions (1 or 0), referred to as binary digits (bits).
Sometimes binary digits are used individually and sometimes
they are used to represent numerical values.

Decimal System

Various number systems are used by PLCs. All number systems
have the same three characteristics: digits, base, weight. The
decimal system, which is commonly used in everyday life, has
the following characteristics:

Ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Base 10

Weights 1, 10, 100, 1000, ...

Binary System

The binary system is used by programmable controllers. The
binary system has the following characteristics:

Two digits 0, 1

Base 2

Weights Powers of base 2 (1, 2, 4, 8, 16, ...)

In the binary system 1s and 0s are arranged into columns. Each
column is weighted. The first column has a binary weight of
20. This is equivalent to a decimal 1. This is referred to as the
least significant bit. The binary weight is doubled with each
succeeding column. The next column, for example, has a weight
of 21, which is equivalent to a decimal 2. The decimal value is
doubled in each successive column. The number in the far left
hand column is referred to as the most significant bit. In this
example, the most significant bit has a binary weight of 27. This
is equivalent to a decimal 128.