Using elementary gates AND, OR$,$ and NOT to build

a circuit model for adding two non$-$negative integers a$,$ b $<8.$ Explicitly, by writing the two

integers as a string of $3$ bits: a $=($x$2,$ x$1,$ x$0),$ and b $=($y$2,$ y$1,$ y$0),$ your addition circuit is to

provide a mapping f : $($x$2,$ x$1,$ x$0,$ y$2,$ y$1,$ y$0)->($z$3,$ z$2,$ z$1,$ z$0)$ such that the output is the binary

representation of integer c $=$ a $+$ b