$\backslash$table$[[$Gate$,$Number of Transistors,t$\_($cd$),$t$\_($pd$)],[$NOT$,2,0\mathrm{.}4,0\mathrm{.}5],[$AND$2,6,2\mathrm{.}2,2\mathrm{.}6],[$OR$2,6,2\mathrm{.}2,2\mathrm{.}6],[$NAND$2,4,1\mathrm{.}8,2\mathrm{.}1],[$NOR$2,4,1\mathrm{.}8,2\mathrm{.}1],[$XOR$2,8,2\mathrm{.}6,3\mathrm{.}2],[$XNOR$2,8,2\mathrm{.}6,3\mathrm{.}2]]$ 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 $d=01$Using only the gates listed in the gate table, implement a transistor$-$minimal hamming distance circuit. The circuit takes four bits of input:

$1$ and $0$: a two$-$bit string $=101$and$0$:atwobitstring$=10$

The circuit produces two bits of output:

$1$ and $0$: a two$-$bit number $=10$ that indicates how many bits differ between $$ and $$

$$ E$.$g$.$thehammingdistancebetween$=00$and$=01$is$=01$