Given four inputs: a$,$ b$,$ c & d$,$ where $($a$,$ b$)$ represents a $2-$bit unsigned binary number X; and $($c$,$ d$)$ represents a $2-$bit unsigned binary number $Y($i$.$e$.$ both $x$ and $Y$ are in the range #$0$ to #$3).$ The output is $z,$ which is $1$ whenever $x>Y,$ and $0$ otherwise $($this circuit is part of a $"2-$bit comparator"$).$ For instance, if $a=1,b=0($i$.$e$.x=b10=>$#$2)$; $c=0,d=1($i$.$e$.Y=b01=>$#$1)$; then $z=1,$ since $b10>$ b$0$Z