Hamming code

Hamming code
Richard Hamming invented at Bell Labs in 1950
Error detection mechanisms by adding a data word (D) with a code, usually a parity check bit (C).
The data stored in length D + C.
Known errors by analyzing the data and parity bits

# Data Bits	# Bit Paritas SEC	# Bit Paritas DEC
8	4	5
16	5	6
32	6	7
64	7	8
128	8	9
512	9	10

Parity check bits are placed with 2N formulation where
Each check bit (C) operates in every bit position data position number 1 in the column contains numbers
Data enter: 00111001 then change the data bits to 3 from 0 to 1 as its error.

how to get the data bits to 3 bits as there are errors?

  N = 0,1,2, ……, while the remaining bits of the data is. Then the exclusive-OR sum::

  C1 = D1 Å D2 Å D4 Å D5 Å D7

  C2 = D1 Å D3 Å D4 Å D6 Å D7

  C4 = D2 Å D3 Å D4 Å D8

  C8 = D5 Å D6 Å D7 Å D8

answer:

Enter data into the formulation of the parity check bits :

C1 = 1 Å 0 Å 1 Å 1 Å 0   = 1

C2 = 1 Å 0 Å 1 Å 1 Å 0   = 1

C4 = 0 Å 0 Å 1 Å 0   = 1

C8 = 1 Å 1 Å 0 Å 0   = 0

Now bit 3 having a data error : 00111101

C1 = 1 Å 0 Å 1 Å 1 Å 0   = 1

C2 = 1 Å 1 Å 1 Å 1 Å 0   = 0

C4 = 0 Å 1 Å 1 Å 0   = 0

C8 = 1 Å 1 Å 0 Å 0   = 0