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# Precedence in different orders associative xyz 000 0

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Unformatted text preview: s that we can perform operations with the same precedence in different orders Associative · · · · xyz · · 000 0 · 0 001 1 1 010 1 1 011 0 0 100 1 1 101 0 0 110 0 0 111 1 1 · 1 2/9/2014 Commutativity lets us reorder the operands for an operation · Commutative x 0 0 1 1 · y 0 1 0 1 y·x 0 0 0 1 0 0 0 1 y ⋅ x 0 0 1 1 y 0 1 0 1 y x y 0 1 1 1 0 1 1 1 x Involution and complementarity deal with variables and their complements ̿ Involution ̅ 1 0 ̅ x+1=1 x 1 x•1 x 1 x+1 x 0 x•0 00 0 01 0 01 1 00 0 10 1 11 1 11 1 10 0 Idempotence tells us that a variable ORed or ANDed with itself is equivalent to the original variable x+x=x x•x=x x x x+x ̅ ̅ 1 ̅ ⋅̅ x•0=0 x 0 x+0 Idempotence x x x•x 00 0 00 0 11 0 1 11 1 ⋅̅ 0 1 1 0 1 0 1 0 1 1 0 0 The distributive identity specifies how a variable AND ITS OPERATOR distribute over a different operator Form 1 Form 2 ⋅ xyz Null x•1=x 1 Complementarity ⋅ x+0=x 0 1 Identity ̅ 0 Identity and null show how variables interact wi...
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