Design a circuit with output f and inputs x0,x1,y0 and y1. Let X = x0x1 be a number, where the four possible values of X, namely 00,01,10,11, represents the four numbers 0,1,2,3 respectively. The same thing with Y = y0y1. The output f should be 1 if the numbers presented by X and Y are equal. Otherwise, f is 0.
Synthesize the simplest possible product of sums expression for f.
By the way, what I did was construct a truth table for all X and Y's, and then create a POS expression for f (Since the solution used the truth table approach, but I have no idea how they get the answer which is
f = (x1+~y1)(~x1+y1)(x0+~y0)(~x0+y0)
My answer which I got from the truth table is
f=(x1+x0+y1+y0)(x1+~x0+y1+~y0)(~x1+x0+~y1+y0)(~x1+~x0+~y1+~y0)
and then I'm stuck. What else can be done to simplify the above expression into the simplest POS form?