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.
What is a 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 |
|---|---|
| 0 | 000 |
| 1 | 001 |
| 2 | 010 |
| 3 | 011 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
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 value | 4-bit code | 10-bit code |
|---|---|---|
| 0 | 0000 | 0000000000 |
| 1 | 0001 | 0000000010 |
| 2 | 0010 | 0000000100 |
| 3 | 0011 | 0000001000 |
| 4 | 0100 | 0000010000 |
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.
References
- 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.