2. F is a function that accepts inputs x {0, 1, 2}, y E {1, 2, 3} and outputs z = max(x2, y). Suppose you use unsigned binary code to encode x, y, and z. x is en- coded as Xixo, y is encoded as yiyo, z is encoded as 222120. (a) (6 Points) Fill the following table (Note: Zazizo should output zero for invalid inputs) 22 21 20 yo 0 Yi 0 0 1 1 1 0 1 21 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 20 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 (b) (12 points) write the sum of minterms and product of maxterms expressions for z (20 = = ..., 21 = ..., Z2 = ..., the boolean variables are {30, X1, yo, y})