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2/17/09
ESE218 Spring 2009 Lecture 7
1
ESE218 Lecture 7. Minterms and Maxterms.
Minimization of expressions with Kmaps.
Outline
±
Canonical
standard forms
±
form minterm and Maxterm numbers
±
conversion
±
Logical adjacency
²
algebraic expression
²
graphical representation
±
Logic minimization with Kmaps
²
2, 3, and 4variable maps
²
5 and 6variable maps
±
Primary implicants and function covers
±
Summary
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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
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 twostep 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.
 Spring '08
 DONETSKY

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