Design a combinational circuit that forms the 2-bit binary sum S1S0 of two 2-bit numbers A1A0 and B1B0 and has both a carry input C0 and carry output C2. Design the entire circuit implementing each of the three outputs with a two-level circuit plus inverters for the input variables. Begin the design with the following equations for each of the two bits of the adder:
S(i) = Ai'Bi'Ci + Ai'BiCi' + AiBi'Ci' + AiBiCi
C(i+1) = AiBi + AiCi + BiCi