Design a circuit with three inputs $($x$,$y and z$)$ representing an unsigned $3-$bit binary representation of a decimal number N$,$ and three outputs $($a$,$ b and c$)$ also representing bits of an unsigned $3-$bit binary number M where M $=($N$+3)$ mod $8.($i$.$e$.,$ the C modulo operator $\%$ and M $=($N$+3)\%8.$ For example, $(2+3)$ mod $8=5$; $(6+3)$ mod $8=1,$ etc.. Show $($a$)$ your truth table, $($b$)$ the Boolean function$($s$)$ for the above circuit, and $($c$)$ the final circuit $($using only OR gates, AND gates, and NOT gates$).$