29. Let the message word = 0  1  1  1.  Use Hamming (4,7) to form the codeword.Group of answer choices0 1 1 1 1 000 1 1 1 0 1 00 1 1 1 1 0 10 1 1 1 0 0 1

The Hamming (7,4) code adds three additional parity bits to every four data bits of the message. The parity bits are inserted into the index positions that are powers of two (i.e., 1, 2, 4, 8, etc.). The parity bits calculate the parity for a set of bits in the code word, including the parity bit itself.

Given the message word 0 1 1 1, we need to add three parity bits (P1, P2, P4) to form the codeword.

1. P1 should be placed at position 1, P2 at position 2, and P4 at position 4. The remaining positions (3, 5, 6, 7) will be filled with the message word bits.

   So, we have P1 P2 0 P4 1 1 1.

2. P1 is calculated as the parity bit for all bits in positions that have the least significant bit in their binary representation set to 1 (positions 1, 3, 5, 7). In our case, these are bits at positions 1, 3, 5, 7 (P1, 0, 1, 1). If we want even parity, P1 should be set to 1 (because we have an odd number of 1's).

   So, we have 1 P2 0 P4 1 1 1.

3. P2 is calculated as the parity bit for all bits in positions that have the second least significant bit in their binary representation set to 1 (positions 2, 3, 6, 7). In our case, these are bits at positions 2, 3, 6, 7 (P2, 0, 1, 1). If we want even parity, P2 should be set to 0 (because we have an even number of 1's).

   So, we have 1 0 0 P4 1 1 1.

4. P4 is calculated as the parity bit for all bits in positions that have the third least significant bit in their binary representation set to 1 (positions 4, 5, 6, 7). In our case, these are bits at positions 4, 5, 6, 7 (P4, 1, 1, 1). If we want even parity, P4 should be set to 1 (because we have an odd number of 1's).

   So, we have 1 0 0 1 1 1 1.

Therefore, the Hamming (7,4) codeword for the message word 0 1 1 1 is 1 0 0 1 1 1 1.