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# lec5 - CS 140 Lecture 5 Professor CK Cheng CSE Dept UC San...

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CS 140 Lecture 5 Professor CK Cheng CSE Dept. UC San Diego 1

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Part I. Combinational Logic 1. Specification 2. Implementation K-map: Sum of products Product of sums 2
Implicant : A product term that has non-empty intersection with on-set F and does not intersect with off-set R . Prime Implicant : An implicant that is not covered by any other implicant . Essential Prime Implicant : A prime implicant that has an element in on-set F but this element is not covered by any other prime implicants . Implicate : A sum term that has non-empty intersection with off-set   and does not intersect with on-set F.  Prime Implicate : An implicate that is not covered by any other implicate. Essential Prime Implicate : A prime implicate that has an element in off-set R but this element is not covered by any other prime implicates . 3

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Example Given F = Σ m (3, 5), D = Σ m (0, 4) 0 2 6 4 1 3 7 5 b c a - 0 0 - 0 1 0 1 Primes: Σ m (3), Σ m (4, 5) Essential Primes: Σ m (3), Σ m (4, 5) Min exp: f(a,b,c) = a’bc + ab’ 4
Five variable K-map 0 4 12 8 c d b e 1 5 13 9 3 7 15 11 2 6 14 10 16 20 28 24 c d b e a 17 21 29 25 19 23 31 27 18 22 30 26 Neighbors of m 5 are: minterms 1, 4, 7, 13, and 21

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