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 Course: Seminar Topic: Seminar Description: Consider a Hamming code to detect and correct for single-bit errors assuming each codeword contains a seven-bit data field, e.g. an ASCII character.
for example. Such a coding scheme requires four check bits since, with this scheme, the check bits occupy all bit positions that are powers of 2.
Such a code is thus known as an block code .
For example, the bit positions of the value 1001101 are:
Bit Position 11 10 9 8 7 6 5 4 3 2 1
Bit value 1 0 0 x 1 1 0 x 1 x x
The four bit positions marked with x are used for the check bits, which are derived as follows. The four-bit binary numbers corresponding to those bit positions having a binary 1 are added together using modulo 2 arithmetic and the four check bits are then the four-bit sum:
11 = 1011
7 = 0111
6 = 0110
3 = 0011
1001
The transmitted codeword is thus:
Bit Position 11 10 9 8 7 6 5 4 3 2 1
Bit value 1 0 0 1 1 1 0 0 1 0 1