PRINCIPLE OF BOOLEAN ALGEBRRA

May 29th, 2015
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Boolean algebra is the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation. Or in simple words, it is algebra of logic. It is one of the most basic tools to analyze and

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BOOLEAN ALGEBRADEFINITION: -Boolean algebra is the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation.Or in simple words, it is algebra of logic. It is one of the most basic tools to analyze and design logic circuits.HISTORY: -Boolean algebra is a form of mathematics developed in 1854 by English mathematician George Boole (18151864). Boole created a system by which certain logical statements can be expressed in mathematical terms.APPLICATIONS: -The original purpose of the algebra was to simplify logic statements and solve logic problems.This concept has roots and applications in logic, set theory, topology, measure theory (measure algebras), functional analysis (algebras of projections), and ring theory (Boolean rings).It also has practical application in telephone switching circuits. Today it is the backbone of design and analysis of computer and other digital circuits.PRINCIPLE OF BOOLEAN ALGEBRRA: -The value of any Boolean variable depends upon so many Boolean variables. Eg: -F = A.B.C. + DHere A, B, C and D are Boolean variables. In above equation the variable F is a function of A, B, C and D. This can be written as F = f (A,B,C,D) A variable in Boolean algebra can take only two values:1 (true)2 (false)BOOLEAN OPERATIONS: There are three basic operations in Boolean algebra1. AND Operations is represented by X.Y2. OR Operations is represented by X+Y3. NOT

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