Acommunication system uses a sec-ded (single error correction-double error detection) code to protect transmissions. the code is based on a 7-bit hamming code extended with an odd parity bit (the most significant bit x8). using the notation from the notes, each received word consists of the parity bit followed by the 7-bit hamming code word x7x6x5x4x3x2x1. for each of the following received words, extract the 4-bit data word when possible, or mention that the received word had uncorrectable errors.
hint: remember that this code is able to correct single errors. if you detect an error and can flip 1 bit to get to a valid codeword, then you have found and fixed the error. if you can't get to a valid codeword with 1 bit flip, then the received word is uncorrectable because there may be more than one way to flip two bits to get to valid codewords.

00101101
1000
10101001
10010001
00111001