Modify the binary comparator shown in the figure so it will compare 2s complement numbers. Let a1 = x1 and b1 = y1. Note that all four combinations of ai and bi are used; 00 indicates that X and Y are positive and equal, 11 indicates that X and Y are negative and equal, 01 indicates X > Y, and 10 indicates X

(a) Derive and complete the transition table for this comparator.

(b) Derive minimal sum-of-product expressions for ai+1 and bi+1.

(c) Derive a circuit for Z1, Z2, and Z3.

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