CS 140 Lecture 5 Professor CK Cheng 10/10/02
Part I. Combinational Logic 1.Spec 2.Implementation K-map: Sum of products Product of sums
Implicant: A product term tat covers at least an element in F and has no intersect with R. Prime Implicants: Largest rectangles that intersect On Set but not Off Set that correspond to product terms. Essential Primes: Prime implicants covering elements in F that are not covered by any other primes.
Example Given F = m (3, 5), D = m (0, 4) c a b Primes: m (3), m (4, 5) Essential Primes: m (3), m (4, 5) Min exp: f(a,b,c) = a’bc + ab’
5 variable K-map d a c b d a c b e Neighbors of 5 are: 1, 4, 13, 7, and 21 Neighbors of 10 are: 2, 8, 10,14, and 26
6 variable K-map d a c b d a c d a c b d a c e f b b
Min product of sums Given F = m (3, 5), D = m (0, 4) c a b Prime Implicates: M (0,1), M (0,2,4,6), M (6,7) Essential Primes Implicates: M (0,1), M (0,2,4,6), M (6,7) Min exp: f(a,b,c) = (a+b)(c )(a’+b’)
Corresponding Circuit a b a’ b’ c f(a,b,c,d)
Another min product of sums example Given R = m (3, 11, 12, 13, 14) D = m (4, 8, 10) K-map d a c b
Prime Implicates: M (3,11), M (12,13), M(10,11), M (4,12), M (8,10,12,14) Essential Primes: M (8,10,12,14), M (3,11), M(12,13)