Which one of the following choices gives the correct values of $x$ and $y$?

In a 12-bit Hamming code with codeword bits numbered from position 1 to position 12 (right-to-left):

$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \text{Bit Position} & 12 & 11 & 10 & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ \hline \text{Bit} & d_8 & d_7 & d_6 & d_5 & c_8 & d_4 & d_3 & d_2 & c_4 & d_1 & c_2 & c_1 \\ \hline \text{Value} & 1 & 1 & 0 & x & y & 0 & 1 & 0 & 0 & 1 & 1 & 0 \\ \hline \end{array}$$

Using even parity for the check bits:

1. Parity bit $c_1$ covers all positions with the $1^{\text{st}}$ bit of their binary index as 1 (positions 1, 3, 5, 7, 9, 11):

   $$c_1 = d_1 \oplus d_2 \oplus d_4 \oplus d_5 \oplus d_7$$

   Substitute the given values ($c_1 = 0, d_1 = 1, d_2 = 0, d_4 = 0, d_5 = x, d_7 = 1$):

   $$0 = 1 \oplus 0 \oplus 0 \oplus x \oplus 1$$

   $$0 = x \implies x = 0$$

2. Parity bit $c_8$ ($y$) covers all positions with the $4^{\text{th}}$ bit of their binary index as 1 (positions 8, 9, 10, 11, 12):

   $$c_8 = d_5 \oplus d_6 \oplus d_7 \oplus d_8$$

   Substitute $x = 0, d_6 = 0, d_7 = 1, d_8 = 1$:

   $$y = 0 \oplus 0 \oplus 1 \oplus 1 = 0$$

Thus, $x = 0$ and $y = 0$, which matches option (A).