16-bit messages are transmitted using a Hamming code. How many check bits are needed to ensure that the receiver can detect and correct single-bit errors? Show the bit pattern transmitted for the message 1101001100110101. Assume that even parity is used in the Hamming code.

Answer: 5 check bits are needed

Explanation:

We know that

m + r + 1 = 2r

For m = 16, r = 5.

Therefore we need 5 check bits for 16-bit messages.

For message 1101001100110101, we know the codeword should be:**1*101*0011001*10101, in which bit 1, 2, 4, 8, 16 are check bits to becomputed.

3 = 1 + 2

5 = 1 + 4

6 = 2 + 4

7 = 1 + 2 + 4

9 = 1 + 8

10 = 2 + 8

11 = 1 + 2 + 8

12 = + 4 + 8

13 = 1 + 4 + 8

14 = 2 + 4 + 8

15 = 1 + 2 + 4 + 8

16 = + 2 + 2 + 4 + 8