Digital Design – Binary Codes

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

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

Binary Code

Suppose we have a 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 minimum 3 bits like in example above,

n = 3 bits so that 23 = 8.

Maximum bit for Binary Code

There is no restriction on 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.

 

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