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 
Rules of Boolean Algebra

  • DEMORGAN'S THEOREMS
    • BOOLEAN ANALYSIS OF LOGIC CIRCUITS 
    • Standard and Canonical Forms
    • CANONICAL FORMS OF BOOLEAN EXPRESSIONS 

    • KARNAUGH MAP MINIMIZATION
    • COMBINATIONAL LOGIC ANALYSIS
    • THE UNIVERSAL PROPERTY OF NAND AND NOR GATES 

    •  FUNCTIONS OF COMBINATIONAL LOGIC
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