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Lec6-canonical (1)

# Lec6-canonical (1) - ECE2030 I ntroduction to Computer...

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Unformatted text preview: ECE2030 I ntroduction 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 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 BC is a minterm in Ā B B 3 3 but not in but not in B B 4 . ABCD is a . ABCD is a minterm in minterm 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. 4 Minterms in B B 3 5...
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Lec6-canonical (1) - ECE2030 I ntroduction to Computer...

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