TongLecture4

# TongLecture4 - CS281 Lecture 4 Tuanjie Tong Last Class...

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CS281 Lecture 4 Tuanjie Tong

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Last Class: Logic Gates and Boolean Algebra This class: Start studying Boolean Algebra in detail.
An Example Implementing XOR…

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Common axioms in defining an algebraic structure Closure: Associativity: Identity Element: Commutativity: Inverse Element: Distributivity: S y x S y x , , ) ( ) ( z y x z y x = x e x x e = = x y y x = e y x = ) ( ) ( ) ( z x y x z y x =
Huntington axioms for Boolen Algebra Axiom 1 (Closure): (a) B is closed with respect to “+”; (b) B is also closed with respect to “.” Axiom 2 (Identity Element): (a) 1 with resepect to “.”; (b) 0 with respect “+” Axiom 3 (Commutativity): (a) B is commutative with respect to 1; (b) B is also commutative with respect to 0

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Algebra (cntd…) Axiom 4 (Distributivity): (a) “.” is distributive over “+”; (b) “+” is distributive over “.” Axiom 5 (Complement element):
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TongLecture4 - CS281 Lecture 4 Tuanjie Tong Last Class...

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