2. Find the sum-of-products expansions of the Boolean function F(x, y, z) that equals 1 if and only if a) x = 0. b) xy = 0. c ) xty = 0. d) xyz = 0.2. Consider the four two-bit integers (00)2, (01)2, (10)2, (11)2, or 0, 1, 2, 3. Your job is to construct a circuit using AND, OR and NOT gates that takes two two-bit integers, (1X0)2 and (y1yo)2 and returns 1 if (120)2 > (y1yo)2 and 0 otherwise. E.g. If x1 = 1, To = 0, y1 = 0, yo = 1, then (x1X)2 = (10)2 = 2 and (y1yo)2 = (01)2 = 1. Since 2 > 1, your circuit would output a 1 in this instance.3. A multiplexer takes a number of different incoming inputs and depending how the control bits are set, passes one of inputs through to the output. A one bit multiplexer has two possible inputs that could be passed through (300 and $1) and one control bit CD. If c0 = 0, then the output of the circuit is the value of 590. If co = 1, then the output of the circuit is :31. A two bit multiplexer has four possible inputs that could be passed through (:50, :61, 51:2, and :53) and two control bits (co and cl). If the control bits are set so that co = 1, cl = 0, then since (6061);; = (10)2 = 2, 962's output would be passed through. Using AND, OR and NOT gates design a) a 1 bit multiplexer. b) a 2 bit multiplexer