A seven-bit Hamming code is received as 1111101. What is the correct code?

Hamming code is used to detect errors. Here the codeword belongs to even parity, So when the data word and the parity bits in check word is even then there is no error.

∴ P₁ P₂ D₃ P₄ D₅ D₆ D₇

    1   1   1   1   1   1   1

C₁ = (1, 3, 5, 7)

     =  1 1 1 1 (Even number of 1's, So no error)

C2 = (2, 3, 6, 7)

    = 1 1 0 1 (Odd number of 1's, So error present)

C2 = (4, 5, 6, 7)

    = 1 1 0 1 (Odd number of 1's, So error present)

∴ Check word C = C₄ C₂ C₁

= 1 1 0 = Decimal 6

Hence error is present at 6th position.

So, New code = 1 1 1 1 1 1 1