Digital Systems Design, Volume I

Numbering Systems and Logical Operations

Larry Massengale

• Publisher: Momentum Press
• Year: 2019
• Print ISBN: 9781949449112
• eBook ISBN: 9781949449129
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

Working as an engineer with advanced weapon systems for more than 25 years, it was crucial to understand the fundamentals of numbering systems, logic gate design, and the logical math known as Boolean Algebra. Whether as a technician or engineer, these fundamentals are the basics of engineering and are essential in interpreting logic gate functionality. The intent of this book is to provide much more information than most commercial engineering references currently offer.

In Chapter 1, numbering systems such as binary, octal, hexadecimal, gray code, binary-coded decimal, and other systems are discussed. Chapter 2 discusses constants and variables, implementing the basic design of truth tables, basic gate operators, and several other logic gate designs. Chapter 3 provides a broad array of Boolean Algebra symbology and logic gate operations, discussing topics such as properties, theorems, implementing and interpreting truth tables from Boolean Algebra expressions, finding minterms and maxterms from symbology expressions, and more. The chapter review and chapter answer sections provide an extensive number of questions with comprehensive insight to showing how to attain the answers. This book will be an extremely valuable asset for technical and engineering students studying digital system design.

CHAPTER 1

NUMBERING SYSTEMS AND CODES

1.1.INTRODUCTION

In the study of digital systems design, digital circuits only understand on and off conditions. The conditions can be represented by logic low and high states. For a Complementary Medal-Oxide Semiconductor (CMOS) gate operating at a power supply voltage of 5 volts, the acceptable input signal voltages range from 0 volts to 1.5 volts for a low logic state and 3.5 volts to 5 volts for a high logic state. Since only two conditions (off and on) must be met in a digital circuit, the binary numbering system (0 and 1) is used.

In the binary (base 2) numbering system, the two logic levels used to represent lows and highs are Logic 0 and Logic 1, respectively. The levels are represented in digital circuits by bits. The word bit was derived from the words binary digit. Since binary is used in all digital systems, a method must be available to convert a decimal number into a binary number. In addition, the reverse procedure is necessary to take the outputs of digital circuits in binary form and make them readable in decimal form.

Two additional numbering systems are often used in addition to the binary system when working with digital circuits. Octal is a base-8 numbering system that utilizes only the digits 0 through 7. Hexadecimal is a base-16 numbering system that uses the digits 0 through 9 and the letters A through F. These two numbering systems provide a method of reducing the bulkier binary numbers.

Some codes have been developed to make circuits user friendly and to improve reliability and operation. Others have been developed for standardization and for detecting errors. We will be discussing these coded ...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Contents
• Abstract
• List of Figures
• List of Tables
• Acknowledgments
• Chapter 1 Numbering Systems and Codes
• Chapter 2 Logic Gates Design
• Chapter 3 Boolean Algebra
• Bibliography
• About the Author
• Index