(Error Detection and Correction)

(a) Using 2d parity, create the matrix for the following data: 1001, 1101, 1111, 0010. Calculate the row, column, and matrix parity (even parity). Explain in detail how it may be possible for errors to go undetected using this method.

(b) Using Hamming(15,11), create the Hamming codeword for the following 11 bit string: 10110010110.

(c) Using Hamming(15,11), check the following codeword for correctness: 101101011101010. If it is correct,show proof by computing the parity bits in the codeword. If it is not correct, compute the correct codeword based on the data associated with the incorrect codeword.