Page 43 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design Nisha Sethi, Lovely Professional University

Notes Unit 3: Boolean Algebra

CONTENTS
Objectives
Introduction
3.1 Boolean Algebra
3.1.1 Boolean Arithmetic
3.1.2 Boolean Algebraic Identities
3.1.3 Boolean Algebraic Properties
3.1.4 Translating Truth Tables into Boolean Expressions
3.1.5 Boolean Rules for Simplification
3.2 Boolean Theorems
3.2.1 Multivariable Theorems
3.3 DeMorgan’s Theorems
3.3.1 Implications of DeMorgan’s Theorems
3.4 Summary
3.5 Keywords
3.6 Review Questions
3.7 Further Reading

Objectives

After studying this unit, you will be able to:
• Explain the Boolean algebra
• Describe the Boolean theorems
• Explain the DeMorgan’s theorems
Introduction

Boolean logic forms the basis for computation in modern binary computer systems. You can
represent any algorithm, or any electronic computer circuit, using a system of Boolean equations.
This provides a brief introduction to Boolean algebra, truth tables, canonical representation, of
Boolean functions, Boolean function simplification, logic design, combinatorial and sequential
circuits, and hardware/software equivalence.
The material is especially important to those who want to design electronic circuits or write
software that controls electronic circuits. Even if you never plan to design hardware or write
software than controls hardware, the introduction to Boolean algebra this unit provides is still
important since you can use such knowledge to optimize certain complex conditional expressions
within IF, WHILE, and other conditional statements.
On minimizing (optimizing) logic functions uses Veitch Diagrams or Karnaugh Maps. The
optimizing techniques this unit uses reduce the number of terms in a Boolean function. You
should realize that many people consider this optimization technique obsolete because reducing
the number of terms in an equation is not as important as it once was. This unit uses the mapping
method as an example of Boolean function optimization, not as a technique one would regularly

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