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(Syndrome parity bits) Derive the formulas for the parity bits x5, x6, x7 of the Hamming [7, 4] code.

(Hamming code error) A message is sent using the [7, 4] Hamming code. The first word received is 0001111, which has no errors.

Assuming that subsequent words are either correct or have at most one error, what are the correct versions of the following received words?
(a) 0101101
(b) 0100111

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