3. For this question we will consider the logic circuit for adding two two-bit numbers. (a) (Graded for fair effort completeness?) Write the input-output definition table for two-bit addition with inputs xo, Yo, X1, Y1 representing (r1x0)2,2 and (y1y0)2,2 and outputs 20, 1, 22 representing (222120)2.3 = (x1x0)2,2 + (y1y0)2.2. Hint: Your table will need 16 rows of input values. Consider how to organize them. (b) In class, we saw that an expression for the circuit output value zo in terms of the input values is Write a logically equivalent compound proposition to this, using the propositional variables xo, Yo and only the propositional connectives A and . Justify your answer using the definition of logical equivalence and either a truth table or a sequence of applications of logical equivalences from class and/or the textbook. (c) (Graded for fair effort completeness) Write a compound proposition that is logically equivalent to the expression for z1 and write a compound proposition that is logically equivalent to the expression for z2, using only the propositional connectives A, V, and . Hint: CNF and DNF may be helpful here