16bit message are transmitted using Hamming code How many ch

16-bit message are transmitted using 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. Assuming that even parity is used in the Hamming code.

Solution

Answer:

It is a 16 bit message , that means check bits are needed at 1 , 2 , 4 , 8 , and 16 . Thus check bits needed are 5 that reciever can detect and correct single bit errors. Now, the bit patterns are :

C1 C21 C4101 C80011001 C1610101

Now , lets do the following

C1 = 1 xor 1 xor 1 xor 0 xor 1xor 0 xor 1xor 1xor 1 xor1 = 0

C2 = 1 xor 0 xor 1 xor 0 xor 1xor 0 xor 1 xor0 xor1 = 1

C4 = 1 xor 0 xor 1 xor1 xor 0 xor 0 xor 1 xor 0 xor1 = 1

C8 =    0 xor 0 xor 1 xor 1 xor 0 xor 0 xor 1 = 1

C16 = 1 xor 0 xor 1 xor 0 xor 1 = 1

The message transmitted is : 011110110011001110101