Badass Boolean Algebra Tut
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Ms Sandhya Rani Dash UNIT 3: INTRODUCTION TO BOOLEAN ALGEBRA Structure 3.1 Introduction 3.2 Objectives 3.3 Logic Levels 3.4 Logic Gates and their Operations 3.4.1 AND operations 3.4.2 OR operations 3.4.3 NOT operations 3.4.5 NAND operations 3.4.6 NOR operation 3.4.7 EX-OR operation 3.4.8 EX-NOR operation 3.4.9 EX-OR operations 3.5 Universal Gates 3.6 Basic Rule, Properties Identities of Boolean Algebra 3.6.1 Complementation law 3.6.2 AND law 3.6.3 OR law 3.6.4 Properties of Boolean algebra 3.7 De Morgan’s Theorem and its Applications 3.8 Logic Minimization using Boolean algebra 3.9 Formulation and Design of simple Logic Circuits 3.10 Sum of Products and Product of Sums 3.10.1 Minterm & Maxterm 3.10.2 Canonical SOP expression 3.10.3 Canonical POS expression 3.11 Unit Summary 3.1 Introduction A new kind of algebra called Boolean algebra or switching algebra is developed by ‘Boole’ in 1854. He stated tha t symbols can be used to represent the structure of logical thoughts . Boolean algebra is a system of mathematical logic, which is governed by certain rules. The variables used in Boolean algebra can have values either 0 or 1. since, we know the digital signals are discrete in nature and can only assume one of the two values 1 (for TRUE/ON/HIGH) and 0 (for FALSE/OFF/LOW) Boolean algebra differs from both the o rdinary algebra and the binary number system. For Example: In Boolean algebra, A + A = A and A∙A=A, since the variable A has only one logical value. In case of ordin ary algebra A+A= 2A and A∙A= A 2 , since
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