6-canonical

6-canonical - Boolean Variables ECE2030 Introduction to...

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8/28/09 1 1 ECE2030 Introduction to Computer Engineering Lecture 6: Canonical Forms 2 ± Boolean Variables 3 ² SOP Form 4 ³ SOP Form Example: Two variables (X and Y) produce 2 x 2 = 4 combinations: (both normal) (X normal, Y complemented) (X complemented, Y normal) (both complemented) Thus there are four minterms of two variables Y X XY Y X Y X
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8/28/09 2 5 ± POS form (dual of SOP form) 6 ² POS Form Example: Two variables (X and Y) produce 2 x 2 = 4 combinations: (both normal) (x normal, y complemented) (x complemented, y normal) (both complemented) Y X + Y X + Y X + Y X + 7 • Examples: Two variable minterms and maxterms. Minterms and maxterms are designated with a subscript The subscript is a number, corresponding to a binary pattern The bits in the pattern represent the complemented or normal state of each variable listed in a standard order. Maxterms and Minterms Index Minterm Maxterm 0 x y x + y 1 x y x + y 2 x y x + y 3 x y x + y 8 Purpose of the Index
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This note was uploaded on 10/20/2009 for the course COE 1 taught by Professor Many during the Spring '09 term at Georgia Tech.

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6-canonical - Boolean Variables ECE2030 Introduction to...

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