quiz3ans - ERG2020A: Digital Logic & Systems (Fall 2007)...

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Quiz #3 Suggested Solution 1. Simplify the following Boolean equations using K-map method. The answer should be in (1) sum-of-products and (2) product-of-sums forms (i.e. 2 answers are required) F ( A, B, C, D, E ) = X m (0 , 5 , 8 , 10 , 13 , 15 , 16 , 24 , 27 , 31)+ X d (2 , 11 , 18 , 21 , 22 , 26 , 28 , 29) Ans: D C B E BC DE D C B E BC DE A’ A 1 1 1 1 1 1 1 1 1 1 d d d d d d d d F = C DE + BDE + C E D C B E BC DE D C B E BC DE A’ A d d d d d d d d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 F = BD + C E + C DE F = ( B + D )( C + E )( C + D + E )
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2. Given the following prime implicant table for F ( Z, Y, X, W ): m0 m1 m2 m3 m8 m11 m13 m15 PI A * * * * PI B * * * PI C * PI D * * PI E * * * PI F * PI G * * (a) Select a minimum cover for the given function Min. cover = PI A + PI E + PI G + PI B Remarks: Using PI D in place of PI B deducts 1 pt (b) Why the number of minterms covered by PI B is not a power of 2? It is because some don’t cares are covered by the prime.
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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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quiz3ans - ERG2020A: Digital Logic & Systems (Fall 2007)...

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