Answer the following questions for the circuit below of F(A, B, C) B Cout + Cin S 0 1 DOO DAL De D MG, MG MG F (a) Fill out the truth table for adder outputs S, Cout, decoder outputs Doo, D01, D10, D1, and inputs to mystery gate MG, and MG. A B s Cout D. DO D10 D11 MG, MG F 0 0 0 0 1 0 0 1 0 0 Olo 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 (b) From the truth table of (a), determine what the mystery gate is (marked MG in the diagram). The answer has to be an exact unambiguous term describing the logical functionality of the mystery gate