Design a digital circuit having inputs ao, a,, b0, b,, whose output is 1 if and only if b b,21 + b,20 is greater than a a1.21 + ao-20. (The + and . dot operators in the preceding sentence are integer rather than Boolean.) Show the truth table and Boolean formula for your circuit. (Hint, it might help to include extra "comment" columns for a and b in your truth table. The values for these columns would be one of the integers 0, 1, 2, 3.)