Hamming Code

Question

Comments

What Is The Ans of this questions.

Answer 1

option D.

only 1st parity bit incorrect.

Answer 2

$D_{12}$	$D_{11}$	$D_{10}$	$D_9$	$P_8$	$D_7$	$D_6$	$D_5$	$P_4$	$D_3$	$P_2$	$P_1$
$1$	$0$	$1$	$0$	$0$	$0$	$0$	$0$	$1$	$0$	$1$	$0$

 

for $P_1$ we check $D_3D_5D_7D_9D_{11}=00000$ Hence $P_1$ should be $0$

for $P_2$ we check $D_3D_6D_7D_{10}D_{11}=00010$ Hence $P_2$ should be $1$

for $P_4$ we check $D_5D_6D_7D_{12}=0001$ Hence $P_4$ should be $1$

for $P_8$ we check $D_9D_{10}D_{11}D_{12}=0101$ Hence $P_8$ should be $0$

Hence the correct codeword should be

$D_{12}$	$D_{11}$	$D_{10}$	$D_9$	$P_8$	$D_7$	$D_6$	$D_5$	$P_4$	$D_3$	$P_2$	$P_1$
$1$	$0$	$1$	$0$	$0$	$0$	$0$	$0$	$1$	$0$	$1$	$0$

 

Hence Option $ 1010\ 0000\ 1010$ is correct answer.

Comments

Why are we checking for D12 while checking for P1. shouldn't we consider D11 because it has 11 has 1 in LSB?

This link here says for P1 we need to check those bit positions which have 1 in them at LSB(3, 5, 7 9, 11), for P2, second from LSB(3, 6, 7, 10, 11) and so on. Using the this logic I got the same code for P2, P3 and P4. So answer turns out to be A  for me.

https://www.geeksforgeeks.org/hamming-code-in-computer-network/

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@Aware1111

yes you are correct by mistake i took $D_{12}$ instead of $D_{11}$, rest were correct but now i am not getting $A$.

please check once more, i updated my answer.