Consider the four two$-$bit integers $(00)2,(01)2,(10)2,(11)2,$ or $0,1,2,3.$ Your job is to construct a circuit using AND, OR and NOT gates that takes two two$-$bit integers, $($x$1$x$0)2$ and $($y$1$y$0)2$ and returns $1$ if $($x$1$x$0)2>($y$1$y$0)2$ and $0$ otherwise. E$.$g$.$ If x$1=1,$ x$0=0,$ y$1=0,$ y$0=1,$ then $($x$1$x$0)2=(10)2=2$ and $($y$1$y$0)2=(01)2=1.$ Since $2>1,$ your circuit would output a $1$ in this instance.