Hamming code

The hamming codes are used extra parity bits to identify a single bit error. To get from one-bit pattern to the other, few bits are to be changed in the data. Such a number of bits can be termed as Hamming distance. It can only detect a single bit error correction. If the parity has a distance of 2, a one-bit flip can be detected. But this can't be corrected. Also, any two-bit flips cannot be detected.

7-bit Hamming code is commonly used which contains 4 data bits and 3 Parity bits.  The position of the parity bit is determined by the formula – 2^n (where n=0,1,2…).

For n=0, the position of first parity, P₁ = 2^0=1

For n=1, the position of first parity, P₂ = 2^1=2

For n=2, the position of first parity, P₄ = 2^2=4

The value of P₁ depends on the data bits D₃, D_5, and D_7.

The value of P₂ depends on the data bits D₃, D_6, and D_7.

The value of P₃ depends on the data bits D₅, D_6, and D_7.

Example: If data is 1011 then find the value of P₁, P₂ & P₄ ( Even parity)?

Solution: The data bit with the corresponding symbol is shown in the table:

7	6	5	4	3	2	1
D7	D6	D5	P4	D3	P2	P1
1	0	1	?	1	?	?

Now, P₁ depends on the data bits D₃, D₅ and D₇ i.e (111) which contains the odd number of 1’s.

So, for even parity P₁ = 1.

P₂ depends on the data bits D₃, D₆ and D₇ i.e (101) which contains the even number of 1’s.

So, for even parity P₂= 0.

P₄ depends on the data bits D₅, D₆ and D₇ i.e (101) which contains the even number of 1’s.

So, for even parity P₃ = 0.