Please include detailed solution with proof, thank you.

2. (a) The following message is received using the 7-digit Hamming Code. Correct any single error that may have occurred during transmission. a a a b b b b 1 0 1 0 1 01 Note that the vertical lines have no mathematical significance. They have been included to make things easier to read. (b) Using the same table as in part (a), what 7-digit codeword would you send if you wanted to communicate the message 0101? (c) The following message is received using the 15-digit Hamming Code. Correct any single error that may have occurred during transmission. a a a a a a a a b b b b b bb b d ddd d dd d 0 1 1 0 1 1 0 1 1 1 0 0 0 1 1 (d) Using the same table as in part (C), what 15-digit codeword would you send if you wanted to communicate the message 0101 1110 001? 2. (a) The following message is received using the 7-digit Hamming Code. Correct any single error that may have occurred during transmission. a a a b b b b 1 0 1 0 1 01 Note that the vertical lines have no mathematical significance. They have been included to make things easier to read. (b) Using the same table as in part (a), what 7-digit codeword would you send if you wanted to communicate the message 0101? (c) The following message is received using the 15-digit Hamming Code. Correct any single error that may have occurred during transmission. a a a a a a a a b b b b b bb b d ddd d dd d 0 1 1 0 1 1 0 1 1 1 0 0 0 1 1 (d) Using the same table as in part (C), what 15-digit codeword would you send if you wanted to communicate the message 0101 1110 001