218L7S09 - ESE218 Lecture 7. Minterms and Maxterms....

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2/17/09 ESE218 Spring 2009 Lecture 7 1 ESE218 Lecture 7. Minterms and Maxterms. Minimization of expressions with K-maps. Outline ± Canonical standard forms ± form minterm and Maxterm numbers ± conversion ± Logical adjacency ² algebraic expression ² graphical representation ± Logic minimization with K-maps ² 2-, 3-, and 4-variable maps ² 5- and 6-variable maps ± Primary implicants and function covers ± Summary
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2/17/09 ESE218 Spring 2009 Lecture 7 2 Standard forms •Canonical SOP and POS •minterm and Maxterm numbers •Form conversions Canonical forms will be used for … •Effective description of a complements to the function •Effective simplification of algebraic expressions
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2/17/09 ESE218 Spring 2009 Lecture 7 3 Canonical SOP is an SOP FORM where each of the product terms contains ALL variables X,Y,Z (either complemented or not complemented). . Canonical standard forms SOP: F = X + YZ’ => INCLUDE MISSING VARIABLES INTO EACH PRODUCT TERM: X(Y+Y’)(Z+Z’)+(X+X’)YZ’ => CANONICAL SOP: XYZ+XYZ’+XY’Z+XY’Z’ +XYZ’+X’YZ’ POS: F = (X+Y)(X+Z’) => INCLUDE MISSING VARIABLES INTO EACH SUM TERM (X+Y+ZZ’)(X+YY’+Z’) => CANONICAL POS: (X+Y+Z)(X+Y+Z’)(X+Y+Z’)(X+Y’+Z’) 3 MAXTERMS describe sets of {XYZ} making F=0: {000} {001} {001} {011} Canonical POS is a product of sum terms where each sum term contains ALL variables . Algorithmic simplification of algebraic expressions can be done effectively with two-step process 1) Consider the function as an SOP or POS such that each term includes ALL variables.
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This note was uploaded on 04/12/2009 for the course ESE 218 taught by Professor Donetsky during the Spring '08 term at SUNY Stony Brook.

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218L7S09 - ESE218 Lecture 7. Minterms and Maxterms....

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