A 7bit codeword in binary value 0 1 0 0 1 0 0 is to be decod

A 7-bit codeword in binary value 0 1 0 0 1 0 0 is to be decoded using a hamming code. Check if there is error or not and if there is, correct data. Write syndrome and data. Show your work!

Solution

For k =4 and n = 7
Parity check equations are
C₁*C₃*C₅*C₇ = 0

C₂*C₃*C₆*C₇ = 0

C₄*C₅*C₆*C₇ = 0

Above codeword gives syndrome vector (1 1 1). So there is error in 7th bit.
Correcting data as 0 1 0 0 1 0 1, now syndrome vector comes out to be null.