Haming code data word 1010 1010 0000 1111 data word 1000 101

Haming code
data word: 1010 1010 0000 1111
data word: 1000 1010 0000 1111
16 bit haming code to find the error.

Solution

data word: 1010 1010 0000 1111 data word: 1000 1010 0000 1111 Hamming Code = 2, detect 1 bit error, not collection. Error correction codes: single error correction: m bits message, r bits for checksum what is the requirement of r? total number of possible codewords 2^(m+r) 2^m valid codewords, each of the 1 bit error must be different code how many 1 bit error code? (m+r)2^m so (m+r)2^m + 2^m < 2^(m+r) --> m+r+1 <= 2^r m = 1 r = 2 m = 2 r = 3 m = 3 r = 3 ..... m = 1000 r = 10 lower bound of number of bits needed, can be achieve using hamming code, (hamming) very smart way of placing the check bits