Hamming Code
Hamming code is a set of error-correction codes that can be used to detect and
correct the errors that can occur when the data is moved or stored from the
sender to the receiver. It is a technique developed by R.W. Hamming for error
correction.
What is Redundant Bits?
Redundant bits are extra binary bits that are generated and added to the
information-carrying bits of data transfer to ensure that no bits were lost
during the data transfer. The number of redundant bits can be calculated using
the following formula:
2^r ≥ m + r + 1
Suppose the number of data bits is 7, then the number of redundant bits can be
calculated using: = 2^4 ≥ 7 + 4 + 1 .Thus, the number of redundant bits= 4
Types of Parity bits
A parity bit is a bit appended to a data of binary bits to ensure that the total
number of 1’s in the data is even or odd. Parity bits are used for error detection.
There are two types of parity bits:
1. Even parity bit: In the case of even parity, for a given set of bits, the number
of 1’s are counted. If that count is odd, the parity bit value is set to 1, making
the total count of occurrences of 1’s an even number. If the total number of
1’s in a given set of bits is already even, the parity bit’s value is 0.
2. Odd Parity bit: In the case of odd parity, for a given set of bits, the number
of 1’s are counted. If that count is even, the parity bit value is set to 1, making
the total count of occurrences of 1’s an odd number. If the total number of
1’s in a given set of bits is already odd, the parity bit’s value is 0.
Algorithm of Hamming Code
Hamming Code is simply the use of extra parity bits to allow the identification
of an error.
Write the bit positions starting from 1 in binary form (1, 10, 11, 100, etc).
All the bit positions that are a power of 2 are marked as parity bits (1, 2, 4,
8, etc).
All the other bit positions are marked as data bits.
Each data bit is included in a unique set of parity bits, as determined its bit
position in binary form. a. Parity bit 1 covers all the bits positions whose
binary representation includes a 1 in the least significant position (1, 3, 5,
7, 9, 11, etc). b. Parity bit 2 covers all the bits positions whose binary
representation includes a 1 in the second position from the least significant
bit (2, 3, 6, 7, 10, 11, etc). c. Parity bit 4 covers all the bits positions whose
binary representation includes a 1 in the third position from the least
significant bit (4–7, 12–15, 20–23, etc). d. Parity bit 8 covers all the bits
