2. (9 points) In this question, you will construct a circuit that takes a pair of fixed width two-bit representations (x1xo)2 and (1yo)2 and computes the four output bits for their integer product. For example, the product of (10)2 and (11)2 is (110)2 and could be computed by long multiplication as 10 This is ito 11 This is yiyo 1 0 +1 0 110 This is the product, whose four output bits will be 0110. a. Express the two-bit output of multiplying yo with (x10)2 as two compound propositions: one for the b. Use part a. and our work in class on adding integers in binary to express each of the four bits of output least significant bit, call it ao, and one of the most significant bit, call it a as compound propositions with inputs To, T1,yo, c. Draw a logic circuit with four inputs and four outputs implementing your design in part b. Note: the logic circuit may include the gates for AND, OR, and XOR, and each gate may have as many inputs as you need