Using only the gates listed in the gate table, implement a transistor$-$minimal hamming distance circuit.

The circuit takes four bits of input:

$x_1$ and $x_0$ : a two$-$bit string $x=x_1{x}_0$

$y_1$ and $y_0$ : a two bit string $y=y_1{y}_0$

The circuit produces two bits of output:

$d_1$ and $d_0$ : a two$-$bit number $d=d_1{d}_0$ that indicates how many bits differ between $x$ and $y$

E$.$g$.$ the hamming distance between $x=00$ and $y=01$ is $d=01$