Question

Data: 10011010, even parity, generate the hamming code

Answer 1

To generate the Hamming code for the given data with even parity, mark the positions for the parity bits, insert the parity bits with the even parity rule, and concatenate the original data and parity bits.

Step-by-step explanation:

To generate the Hamming code for the given data with even parity, follow these steps:

1. Write down the original data: 10011010.
2. Count the number of bits in the data. In this case, there are 8 bits.
3. Determine the number of parity bits needed based on the formula: 2^r >= m + r + 1, where r is the number of parity bits and m is the number of data bits. In this case, 2^r >= 8 + r + 1. By trial and error, we find that 4 parity bits are needed.
4. Mark the positions for the parity bits in the data: P1, P2, P4, and P8. These positions correspond to powers of 2 (1, 2, 4, and 8).
5. Insert the parity bits at their respective positions, with their values determined by the even parity rule. For example, P1 = 1 XOR 1 XOR 0 XOR 0 XOR 1 XOR 1 XOR 0 = 0.
6. The final Hamming code is obtained by concatenating the original data and the parity bits. In this case, the Hamming code is 01001110010.