4a_Karnaugh_Maps_Slides - ECE 3504 ECE 3504 Digital Design...

Unformatted text preview: ECE 3504 ECE 3504 Digital Design 1 Digital Design 1 Section 4a: Logic Minimization using Karnaugh Maps What You Should What You Should Already Know! Already Know! • The correct representation of a The correct representation of a four-variable Karnaugh map. • The basic principles of Karnaugh mapping. Minterms and Maxterm Minterms and Maxterm Minterms and Maxterms Minterms and Maxterms • A litera is an expression of one A literal is an expression of one form of a variable. A literal can be uncomplemented (B) or l t d ( B ) complemented (B ′ ). • A minterm of n variables is a product term where a literal form of each variable appears exactly once. A t f i bl i • A maxterm of n variables is a sum term where a literal form of each variable appears exactly once. Minterms and Maxterm Minterms and Maxterm Minterms and Maxterms Minterms and Maxterms A B C f Minterm Form Maxterm Form 0 0 0 0 1 m = A ′ B ′ C ′ M = A+B+C 1 0 0 1 1 m 1 = A ′ B ′ C M 1 = A+B+C ′ 2 1 m 2 = A ′ BC M 2 = A+B ′ +C 2 1 m 2 A BC M 2 A B C 3 0 1 1 0 m 3 = A ′ BC M 3 = A+B ′ +C ′ 4 1 0 0 1 m 4 = AB ′ C ′ M 4 = A ′ +B+C 5 1 0 1 0 m 5 = AB ′ C M 5 = A ′ +B+C ′ 6 1 1 0 1 m 6 = ABC ′ M 6 = A ′ +B ′ +C 7 1 1 1 1 m 7 = ABC M 7 = A ′ +B ′ +C 7 1 1 1 1 m 7 ABC M 7 A B C Karnaugh Map Karnaugh Map Karnaugh Maps Karnaugh Maps CD 00 01 11 10 00 1 3 2 01 AB 01 4 5 7 6 11 12 13 15 14 10 8 9 1 1...
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