# Binary Number System

## What is binary number system?

The binary number system is base-2 system. There are only two digits 0 and 1 which forms any binary number. All computers understand binary logic. Means any kind of data is converted to binary format before it is processed by the computer.Binary number system is a positional weighted number system. It means positional weights and values are associated with it. The weights assigned to a binary number are as follows, ......2

^{3}, 2

^{2}, 2

^{1}, 2

^{0}, 2

^{-1}, 2

^{-2}, 2

^{-3},.....

Since there are only two digits 0 and 1. The number of bits 'n' required to successfully represent 'm' decimal numbers in binary system is given by m=2

^{n}.

We can represent any decimal number as sum of product of weight associated with each bit and the bit itself.

**For example**, consider 1000. Then decimal number corresponding to this binary data is 1 x 2

^{3}+ 0 x 2

^{2}+ 0 x 2

^{1 }+ 0 x 2

^{0 }= 8 + 0 + 0 + 0 = 8

Now consider a fractional binary 100001.10, here the decimal number is

1 x 2

^{5}+ 0 x 2

^{4}+ 0 x 2

^{3 }+ 0 x 2

^{2}+ 0 x 2

^{1}+ 1 x 2

^{0}+ 1 x 2

^{-1}+ 0 x 2

^{-2}

=32 + 0 + 0 + 0 + 0 + 1 + 0.5 + 0

= 33.5

When we have to represent very large decimal number in binary, it becomes very lengthy and inconvenient. Also there is chance of making mistake. Thus, more convenient number systems are used. Refer Hexadecimal Number System.