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Ab 15 10132011 absorptionlaws example10 ptabacabc

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Unformatted text preview: "+" and "." • such that for every element x and y BS • the operations x bar (not x), x + y and x . y are uniquely defined AND NOT • The unary operator not is defined by the relation • The not operator is complement • x is the complement of x also called the • • • • • The and operator is defined by 0 . 0 = 0 0 . 1 = 0 1 . 0 = 0 1 . 1 = 1 12 10/13/2011 OR • • • • • Single variable theorems The or operator is defined by 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 1 Commutative laws Associative laws • A ∙ B = B ∙ A • A + B = B + A • Gate: input order doesn’t matter 13 10/13/2011 Associative laws • (A ∙ B) ∙ C = A ∙ (B ∙ C) = A ∙ B ∙ C • (A + B) + C = A + (B + C) = A + B + C • Gate: multiple input gates defined Distributive laws A ∙ (B + C) = (A ∙ B) + (A ∙ C) and A + (B ∙ C) = (A + B) ∙ (A + C) A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C B+C A.B A.C A ∙(B + C) (A ∙ B) + (A ∙ C) 00 0 0 0 0 11 0 0 0 0 01 0 0 0 0 11 0 0 0 0 00 0 0 0 0 11 0 1 1 1 01...
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This note was uploaded on 05/05/2013 for the course ELEC 1111 taught by Professor Jayashriravishankar during the One '11 term at University of New South Wales.

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