Design a circuit with output f and inputs x0,x1,y0 and y1. Let X = x0x1 be a num
ID: 1831805 • Letter: D
Question
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?
Thanks.
Explanation / Answer
Truth table X Y f X1 X0 Y1 Y0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 Logic expression f = Sm(0,5,10,15) f = X1'X0'Y1'Y0'+ X1'X0Y1' Y0 +X1X0'Y1 Y0' + X1X0Y1Y0 This is the simplifeid equation Logic diagram 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 Logic expression f = Sm(0,5,10,15) f = X1'X0'Y1'Y0'+ X1'X0Y1' Y0 +X1X0'Y1 Y0' + X1X0Y1Y0 This is the simplifeid equation Logic diagramRelated Questions
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