quiz2ans - ERG2020A: Digital Logic & Systems (Fall...

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Quiz #2 Suggested Solution 1. Reduce the following Boolean functions to a minimum SOP form. (use Boolean Algebraic rules only). (a) F ( W, X, Y, Z ) = WX ( Z + Y Z ) + X ( W + WY Z ) = WX + Z + Y + X ( W + Y Z ) = WX + Z + Y + XW + XY Z = X + Y + Z (b) F ( A, B, C, D ) = ( AB + A B )( C D + CD ) + AC = ( AC + AB + A B )( AC + C D + CD ) = ( A + C + AB + A B )( A + C + C D + CD ) = ( A + C + B )( A + C + D ) = A + C + BD (c) Let P = ( Y Z + Y Z ), then P = ( Y + Z )( Y + Z ) = Y Z + Y Z F = WXP + W X P F = ( W + X + P )( W + X + P ) F = WX + WP + W X + XP + W P + X P F = WX + W X + W Y Z + WY Z + W Y Z + WY Z + X Y Z + XY Z + X Y Z + XY Z 2. Obtain the truth table of the following function F , and express the function in sum-of-minterms and product-of-maxterms forms. F ( A, B, C ) = ( A + B )( B + C ) A B C A + B B + C F 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 F = m (0 , 1 , 3 , 7) = Q M (2 , 4 , 5 , 6)
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3. Plot the following function
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This note was uploaded on 05/18/2010 for the course ENGINEERIN ERG2020A taught by Professor Leekinhong during the Spring '07 term at CUHK.

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quiz2ans - ERG2020A: Digital Logic & Systems (Fall...

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