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MIDW07_ANS

# MIDW07_ANS - ECSE-323 Department of Electrical and Computer...

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The prime implicants of the function F(A,B,C,D) = m(0,4,6,7,10,11,15) are given below. (5 points) a) Produce the covering table of the minterms of F and give the essential prime implicants. (5 ponts) b) Apply the Petrick function to the reduced covering table and give ALL minimal two-level sum-of-products expressions of F. ___________________________________________________________________________ ANSWER: Prime implicants Covering table A B C D P1: (7,15) - 1 1 1 P2: (11,15) 1 - 1 1 P3: (10,11) 1 0 1 - P4: (0,4) 0 - 0 0 P5: (4,6) 0 1 - 0 P6: (6,7) 0 1 1 - Essential prime implicants: P3 = A f8e5 B C P4 = f8e5 A f8e5 C f8e5 D Reduced covering table Petrick function corresponding to the reduced table P R = (P5 + P6)(p1 + P6)(P1 + P2) = (P1P5 + P6) (P1 + P2P6) = P1P5 + P1P6 + P2P6 + P1P2P5P6. Minimal two-level sum-of-products expressions: F min = P3 + P4 + P1 + P5 ; F min = P3 + P4 + P1 + P6; F min = P3 + P4 + P2 + P6 F min = A f8e5 B C + f8e5 A f8e5 C f8e5 D + B C D + f8e5 A B f8e5 D F min = A f8e5 B C + f8e5 A f8e5 C f8e5 D + B C D + f8e5 A B C F min = A f8e5 B C + f8e5 A f8e5 C f8e5 D + A C D + f8e5 A B C. Your Name_______________________________________________________ Question 2 : Application of Boolean Logic Theory (10 points) A B C D 0 4 6 7 10 11 15 P1: (7,15) - 1 1 1 x x P2: (11,15) 1 - 1 1 x x P3: (10,11) 1 0 1 - x x P4: (0,4) 0 - 0 0 x x P5: (4,6) 0 1 - 0 x x P6: (6,7) 0 1 1 - x x A B C D 0 4 6 7 10 11 15 P1: (7,15) - 1 1 1 x x P2: (11,15) 1 - 1 1 x x P3: (10,11) 1 0 1 - x x P4: (0,4) 0 - 0 0 x x P5: (4,6) 0 1 - 0 x x P6: (6,7) 0 1 1 - x x A B C D 6 7 15 P1: (7,15) - 1 1 1 x x P2: (11,15) 1 - 1 1 x P5: (4,6) 0 1 - 0 x P6: (6,7) 0 1 1 - x x
(4 points) a)

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• Winter '07
• redacka
• Logic gate, Combinational circuit design, Name_______________________________________________________ Question

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