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Host A transmits 12-bit Hamming code whose hexadecimal value is OxE5F arrives to Host B who is at the receiver end. The medium through the code has been transmitted is not error free but cannot damage parity bit and parity bits has been inserted from left to right at their respective positions. What was the original value Host A transmitted in hexadecimal, (Assume that not more than 1 bit is in error.)
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Error will be in 5th or 10th bit depending on whether the question follows odd parity or even parity.

Any options given? AB or EF
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The code word received by B is :

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

$P_1 : P_1 D_3 D_5 D_7 D_9 D_{11}$ =110011

Even no. of 1's. By default we take even parity.

So no error at $P_1$ 0

$P_2 : P_2 D_3 D_6 D_7 D_{10} D_{11}$ =111011

Odd no. of 1's. So 1

$P_4 : P_4 D_5 D_6 D_7D_{12}$ =00101

Even 1's . So 0

$P_8 : P_8 D_9 D_{10} D_{11} D_{12}$ =11111

Odd 1's. So 1.

So the error is at $P_8P_4P_2P_1$ = 1010 = 8x1 + 2x1 =10. Error at $10^{th}$ bit.

Data word is : $D_3D_5D_6D_7D_9D_{10}D_{11}D_{12}$ = 10101011 = 0xAB

0

Thank you