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Module 6: Information Coding and Decoding

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A (7,4) Hamming code is used for error correction. If the received codeword is 1011010, determine the original data and correct the error.

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Answer

Hamming (7,4): Parity bits at 1,2,4. Received 1011010, even parity checks: p1=1⊕1⊕0⊕0=0p_1=1\oplus1\oplus0\oplus0=0, p2=0⊕1⊕1⊕0=0p_2=0\oplus1\oplus1\oplus0=0, p4=1⊕0⊕1⊕0=0p_4=1\oplus0\oplus1\oplus0=0 syndrome 000 → no error. Data bits 3,5,6,7 =1010. If odd parity syndrome 111 → position 7 error. Method: syndrome binary = error position, flip.

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