CPE 004.pdf - 2.1 2.2 Introduction Basic Definitions*Binary...

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2.1 - 2.2 Introduction, Basic Definitions *Binary Operator - defined on a set S of element is a rule that assigns to each pair of elements from S, a unique element from S. *Set - of elements is any collection of objects usually having a common property. 2.3 Axiomatic Definition of Boolean Algebra *In 1854 , George Boole - Boolean Algebra *In 1938, Claude E. Shannon - Switching Algebra (two-valued Boolean Algebra or Binary Logic) * Boolean algebra - algebraic structure defined by a set of elements, B, together with two binary operators ( addition and multiplication). Complement: x + x' = 1, x * x' = 0 (Baliktad!) Distributive Law: x + (y*z) = (x + y) * (x + z) (Nadidistribute ang plus!) 2.4 Basic Theorems and Properties of Boolean Algebra *Duality Principle: an important property of Boolean algebra that states that every algebraic expression deducible from the postulates of Boolean Algebra remains valid if the *If true, replace AND with OR and replace 1's by 0's. operators and the identity elements are interchanged. Basic Theorems: 2.5 Boolean Functions *Literal = variable on each term Skipped 2.6 to 2.7 Boolean Algebra and Logic Gates (Chapter 2) CPE 004 Page 1

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3.1 Introduction
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