EECS 270 Lecture 10. K-map “rules” – Only circle adjacent cells (remember edges are adjacent!) – Only circle groups that are powers of 2 (1, 2,

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Presentation transcript:

EECS 270 Lecture 10

K-map “rules” – Only circle adjacent cells (remember edges are adjacent!) – Only circle groups that are powers of 2 (1, 2, 4, 8, …) – Only circle 1-cells

Covering g = input combinations for which g outputs 1 Space of all 2 n input combinations (minterms) f = input combinations for which f outputs 1 f covers g if f=1 whenever g=1 f ≥ g

Implicants g = input combinations for which g outputs 1 h f = input combinations for which f outputs 1 If g is a product term & g≤f, Then g is an implicant of f. Space of all 2 n input combinations (minterms) = input combinations for which h outputs 1

Prime Implicants Removing a literal from any product term (any implicant) makes it cover twice as many minterms. – Removing a literal “grows” the term – ex. 3 variables:ab’c covers 1 minterm ab’ aceach cover 2 minterms b’c f ab’c ab’ ac b’c Any way of removing a literal makes ab’c no longer imply f. So ab’c is a prime implicant of f. Any way of removing a literal makes ab’c no longer imply f. So ab’c is a prime implicant of f. ab’c is an implicant of f.

Implicant: Any product term that implies a function F (i.e., if, for some input combination, product term P = 1, then F = 1 for the same input combination) Prime Implicant: An implicant such that if one literal is removed, the resulting product term no longer implies F Essential Prime Implicant: A prime implicant that covers a minterm that is not covered by any other prime implicants Theorem: The minimal SOP of a function is a sum of prime implicants These are only a few of the implicants of this function…