Consider a 2-bit comparator that compares two 2-bit unsigned integers X=x1x0 and Y=y1y0. The circuit produces a single bit F as the output. The output F is 1 if X is less than or equal to Y (i.e. XY ), and 0 otherwise. a) Complete the following truth table for the output F. (4 points) b) Derive the logic function for the output F in the inputs x1,x0,y1, and y0 in both Sum-of-Product ( SoP) and Product-of-Sum (PoS) formats with minterm and maxterm respectively. ( 6 points) c) Given the SoP presentation of output F derived in b), draw K-map, circle groups of 1 s, and then derive the simplest logic function of F. (7 points) d) Draw the circuit corresponding to the simplified logic function of F derived in c), using AND, OR, NOT gates only. Clearly indicate the inputs xI,x,y1, and y0 and the output F in the circuit. ( 3 points)