Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check…

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is \(d_8 d_7 d_6 d_5 c_8 d_4 d_4 d_3 d_2 c_4 d_1 c_2 c_1\),where the data bits and the check bits are given in the following tables:

\(\overset{\textbf{Data bits}}{\begin{array}{|c|c|c|c|} \hline d_{8} & d_{7} & d_{6} & d_{5} & d_{4} & d_{3} & d_{2} & d_{1} \\\hline 1 & 1 & 0 & x & 0 & 1 & 0 & 1 \\\hline \end{array}}\qquad \overset{\textbf{Check bits}}{\begin{array}{|c|c|c|c|} \hline c_{8} & c_{4} & c_{2} & c_{1} \\\hline y & 0 & 1 & 0 \\\hline \end{array}}\)

Which one of the following choices gives the correct values of \(x\) and \(Y\) ?