Q29

Assume that a $12$-bit Hamming codeword consisting of $8$-bit data and $4$ check bits is $d_8d_7d_6d_5c_8d_4d_ 4d_3d_2c_4d_1c_2c_1$, 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 $y$?