prfinal_2003_sol

prfinal_2003_sol - Name ECE-200 Intelligent Systems Spring...

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Name ______________________________________ ECE 200 Intelligent Systems Midterm Exam Page 1 ECE-200 Intelligent Systems Spring 2003 Pracice Final Solution All problems have the same weight Problem 1. We are working with a multiplexor that is to switch between four sources (inputs), each one two bits wide. The multiplexor is to have a single active-low enable, and a non-inverting outputs. (a) Tabulate all inputs and outputs of the circuit. Give signal names and short descriptions. D00 through D31: four data sources, each two bits. D00 and D01 are the two bits for source 0, etc. S0, S1: select inputs ENB: enable input Y0, Y1: outputs (b) Construct the truth table. Use the signal names from part (a) ENB S1 S0 Y1 Y0 0 x x 0 0 1 0 0 D01 D00 1 0 1 D11 D10 1 1 0 D21 D20 1 1 1 D31 D30 Problem 2. The equivalence function of two variables is equal to 1 whenever the two variables are equal, and is 0 otherwise. It is sometimes called the XNOR function, and is written as X Y . (a) Construct a truth table for the equivalence function, and write it as a product of sums. (b) Prove that (X Y) (Y Z) = (X Z) . You may use any method you like for the proof. Proof by finite induction. Let F = (X Y) (Y Z), G = X Z X Y Z X Y Y Z F G 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1
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ECE 200 Intelligent Systems Final Exam Page 2 Problem 3. Given that F(W,X,Y,Z) = S (0,2,8,10,11,13,15). (a)Find the prime implicants of this function.
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