Switching Theory and Logic Design CS203 Module-2 Note

CS203 Switching Theory and Logic Design Second Module Full Note

Module 2-Syllabus

Introduction — Postulates of Boolean algebra – Canonical

and Standard Forms — logic functions and gates

methods of minimization of logic functions — Karnaugh

map method and QuinMcClusky method

Product-of-Sums Simplification — Don’t-Care

Conditions.

BOOLEAN ALGEBRA AND LOGIC SIMPLIFICATION

BOOLEAN OPERATIONS AND EXPRESSIONS

Variable, complement, and literal are terms used in Boolean algebra. A variable is a symbol used to represent a logical quantity. Any single variable can have a 1 or a 0 value. The complement is the inverse of a variable and is indicated by a bar over variable (overbar). For example, the complement of the variable A is A. If A = 1, then A = 0. If A = 0, then A = 1. The complement of the variable A is read as "not A" or "A bar." Sometimes a prime symbol rather than an overbar is used to denote the complement of a variable; for example, B' indicates the complement of B. A literal is a variable or the complement of a variable.
Boolean

Boolean Addition
Boolean Multiplication

LAWS AND RULES OF BOOLEAN ALGEBRA

Laws of Boolean Algebra
Commutative Laws
►The commutative law of addition for two variables is written as A+B = B+A
►The commutative law of multiplication for two variables is A.B = B.A
Associative Laws :
►The associative law of addition is written as follows for three variables: A + (B + C) = (A + B) + C
►The associative law of multiplication is written as follows for three variables: A(BC) = (AB)C
Distributive Law:
►The distributive law is written for three variables as follows: A(B + C) = AB + AC