2-Mod2_LS_2011

2-Mod2_LS_2011 - ECE 270 Introduction to Digital System...

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ECE 270 Introduction to Digital System Design © 2011 by D. G. Meyer 1 Lecture Summary – Module 2-A Reference: Text (4 th Ed.), pp. 183-199; (3 rd Ed.), pp. 193-209 overview o Boole and Shannon o defn – axiom (postulate) o notation – prime ( ) o operator precedence five axioms completely define switching algebra o (A1) existence of two elements o (A2) complement o (A3) AND with 0 / OR with 1 o (A4) AND with 1 / OR with 0 o (A5) AND of 0 with 1 / OR of 0 with 1 duality o defn o key principle theorems o defn o use of perfect induction to prove single-variable theorems o identities o null elements o idempotency o involution o complements
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ECE 270 Introduction to Digital System Design © 2011 by D. G. Meyer 2 two- and three-variable theorems o commutivity o associativity o distributivity o covering o combining o consensus n-variable theorems o generalized idempotentcy o DeMorgan’s law o generalized DeMogan’s law equivalent circuits based on DeMorgan’s law standard forms o defn – literal o defn – product term and SoP expression
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2-Mod2_LS_2011 - ECE 270 Introduction to Digital System...

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