# Digital Design – Binary Codes

Binary codes are used to represent the distinct discrete element of information. They are patterns of 1s and 0s for a computer to understand information other than binary numbers.

The discrete elements of information are not only binary numbers but also, other types of information such as decimal numbers, etc.

## Binary Code

Suppose we have an n-bit code then there are 2n combination of binary codes consists of 1s and 0s.

For example,

3-bit code has 23 = 8 codes

Bit Combination Codes
0000
1001
2010
3011
4100
5101
6110
7111

There are 8 combinations, but the bit combination has value is between 0 to 2n – 1. A 3-bit code has bit combination from 0 to 23 – 1 = 7.

## Minimum bits required

For 16 code combinations, you need minimum of 4 bits, n = 4 bits, so that 24 = 16.

For 8 codes, you need a minimum of 3 bits like in the example above,

n = 3 bits so that 23 = 8.

## Maximum bit for Binary Code

There is no restriction on a number of bits that you can use for a binary code.

For example

10 decimal numbers – 0,1,2,3,4,5,6,7,8,9 can be represented using 4-bits and can also be represented using 10-bits. Let’s check this for first 5 decimal numbers.

Decimal value4-bit code 10-bit code
000000000000000
100010000000010
200100000000100
300110000001000
401000000010000

A 4-bit code is binary representation of decimal and 10-bit code uses placeholder for each decimal number. Here the code – 0000010000 does not mean 25 = 16, but it means 5th position from right is a 1, therefore, decimal number = 4.

## Bibliography

John.F.Wakerly. 2008. Digital Design: Principles And Practices, 4/E. Pearson Education, India.

Mano, M. Morris. 1984. Digital Design. Pearson.

NATARAJAN, ANANDA. 2015. Digital Design. PHI Learning Pvt. Ltd.