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Lec6-canonical (2)

# Lec6-canonical (2) - ECE2030 Introduction to Computer...

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ECE2030 Introduction to Computer Engineering Lecture 6: Canonical (Standard) Forms Prof. Hsien-Hsin Sean Lee Prof. Hsien-Hsin Sean Lee School of Electrical and Computer Engineering School of Electrical and Computer Engineering Georgia Tech Georgia Tech

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2 Boolean Variables A multi-dimensional space spanned by a set of n Boolean variables is denoted by B B n A literal literal is an instance (e.g. A) of a variable or its complement ( ) Ā
3 SOP Form A product of literals is called a product term product term or a cube cube (e.g. ·B·C in Ā B B 3 , or B·C in B B 3 ) Sum-Of-Product (SOP) Sum-Of-Product (SOP) Form: OR OR of product terms, e.g. B+AC Ā A minterm minterm is a product term in which every literal (or variable) appears in B B n BC is a minterm in Ā Ā B B 3 3 but not in but not in B B 4 . ABCD is a minterm . ABCD is a minterm in in B B 4 . . A canonical canonical (or standard standard) SOP function: SOP function: a sum of minterms corresponding to the input combination of the truth table for which the function produces a “ 1” 1” output.

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4 Minterms in B B 3
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