P1 (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 b such that b=3+a if p=0 and produces b=5-a if p=1. b: design a circuit that produces a 6-bit integer c such that c=3a if p=0 and produces c=5a+1 if p=1. c: design a circuit that outputs 6-bit integer d such that d=b if q=0 and d=c if q=1. p2 (20 point