Question

an 8-bit byte with binary value 10101111 is to be encoded using an even-parity hamming code. what is the binary value after encoding?

Answer 1

In even-parity Hamming code, an extra parity bit is added to the data bits to ensure that the total number of 1s in the code word is even.

Step-by-step explanation:

The correct answer is option 10101111001.

In even-parity Hamming code, an extra parity bit is added to the data bits to ensure that the total number of 1s in the code word is even. Here's how the encoding process works:

1. Count the number of 1s in the original 8-bit byte. In this case, there are 5 1s.
2. Choose a position for the parity bit. In even-parity Hamming code, the parity bit is placed in the position that corresponds to the power of 2 (starting from 1) that is greater than or equal to the total number of bits plus the parity bit. In this case, the total number of bits is 8 and the nearest power of 2 is 8. So, the parity bit is placed in the 8th position.
3. Insert the original bits and the parity bit into their respective positions in the code word. The original bits are placed in positions that are not powers of 2, and the parity bit is placed in the 8th position.

So, the binary value after encoding the 8-bit byte 10101111 using even-parity Hamming code is 10101111001.