X Y XY X+Y (X+Y) nor Y (XY) + [(X+Y) nor Y] = F2001Summer CS147 Quiz 1 Name:____________Prof. Sin-Min LeeSection 1 1. (3 points) Construct the truth table for the following combination of gates:Answer: Since therefore we have A B (A n B) A n (A n B) (A n B) n B [A n(A n B)] n [ (A n B) n B]= C 0 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 02. (2 points) Simplify the following Boolean function by K-map.Answer:3. (2 +1 = 3 points) a. Prove that the following two circuits are equivalent by constructing the truth table for each one:b. State the above theorem in Boolean algebraAnswer: Distributive Law 4. (2 points) Prove the theorem X+ XY = X in Boolean algebra bya. Algebraic method.b. Truth tableAnswer: a. LHS = X1 + XY = X( 1+Y) = X 1 = X =RHS. b. X Y XY X+XY 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 12001Summer CS147 Quiz 1 Name:____________Prof. Sin-Min LeeSection 2.1. (3 points) Construct the truth table for the following combination of gates:Answer: X Y XY X+Y (X+Y) nor Y (XY) + [(X+Y) nor Y] = F 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 0 12. ( 2 points) Simplify the following Boolean function by K-map.Answer:3.(1 + 2 =3 points) a.What does the following circuit implement? X Z b. Design the circuit by NAND gates only.4.(2 points) Prove the theorem X+ XY = X in Boolean algebra byc. Algebraic method.d. Truth tableAnswer: a. LHS = X1 + XY = X( 1+Y) = X 1 = X =RHS. b. X Y XY X+XY 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1
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