Page 59 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design Nisha Sethi, Lovely Professional University

Notes Unit 4: Minimization of Boolean Algebra

CONTENTS
Objectives
Introduction
4.1 Minterms and Maxterms
4.2 Sum of Products and Product of Sums Forms of Logic Expressions
4.2.1 Sum of Products Form
4.2.2 Product of Sums Form
4.3 Karnaugh Maps
4.3.1 Karnaugh Map Format
4.3.2 Looping
4.4 Summary
4.5 Keywords
4.6 Review Questions
4.7 Further Reading

Objectives

After studying this unit, you will be able to:
• Explain the minterms and maxterms
• Understand sum of product and product of sum
• Discuss the Karnaugh map
Introduction

Boolean expression is expressed in terms of either sum of product or product of sum. With the sum
of product method the design starts with a truth table that summarises the desired input-output
condition. The next step is to convert the truth table into an equivalent sum of product equation.
Product of sum equation, you can simplify it with Boolean algebra. Alternatively, you may prefer
simplification based on the Karnaugh map. Introduces two standard forms of expressing Boolean
functions, the minterms and maxterms, also known as standard products and standard sums
respectively. A procedure is also presented to show how one can convert one form to the other.
Karnaugh maps are used for many small design problems. It is true that many larger designs are
done using computer implementations of different algorithms. However designs with a small
number of variables occur frequently in interface problems and that makes learning Karnaugh
maps worthwhile. In addition, if you study Karnaugh maps you will gain a great deal of insight
into digital logic circuits.
A Karnaugh map comprises a box for every line in the truth table; the binary value for each box
is the binary value of the input terms in the corresponding table row.

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