A 15-bit Hamming code requires how many parity bits

Electrical Engineering XYZ MCQs

A 15-bit Hamming code requires how many parity bits:

1. 5 parity bits
2. 15 parity bits
3. 4 parity bits
4. None of these

Correct answer: 3. 4 Parity bits

Explanation: Hamming Code uses multiple parity bits. It can detect and correct error bits.
A Hamming Code with n parity bits can have up to 2ⁿ – n – 1 data bits, making a maximum code length of 2 – 1 bits.

Four parity bits can check up to 11 data bits, making a 15-bit code.

Formulas:

Parity bits = n

Total bits = 2ⁿ – 1

If parity bits = 4, then total bits = 2ⁿ – 1 = 2⁴ – 1 = 16 – 1 = 15

Hence 15 bits hamming code requires 4 parity bits.