P$5(15$ points$)$: Given a $3-$bit input A$,1-$bit input P$,1-$bit input Q$,$ a $6-$bit adder, some $2-$to$-1$ MUXes, some NOT gates, and some XOR gates: A$.$ Design a circuit that produces a $6-$bit integer X such that B$=6+2$ A if P$=0$ and produces B$=8-2$ A if P$=1.$ B$.$ Design a circuit that produces a $6-$bit integer Y such that C$=5$A if P$=0$ and produces C$=9$ A$+1$ if P$=1.$ C$.$ Design a circuit that outputs $6-$bit integer such that D$=$B if Q$=0$ and D$=$C if Q$=1.$