DIGITAL FUNDAMENTALS AND APPLICATIONS

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2 DIGITAL FUNDAMENTALS AND APPLICATIONS By Dr. C. K. CHANDA B.E. (Hons.), M.Tech (IIT), Ph.D., LMISTE, FIE (I), Chartered Engineer Professor, Department of Electrical Engineering Bengal Engineering and Science University Shibpur, Howrah West Bengal SUMIT BANERJEE B.E. (Hons.), M.E., (Ph.D.), LMISTE, MIEEE, MIE (I), Chartered Engineer Assistant Professor, Department of Electrical Engineering Dr. B.C. Roy Engineering College, Durgapur, West Bengal UNIVERSITY SCIENCE PRESS (An Imprint of Laxmi Publications Pvt. Ltd.) BANGALORE CHENNAI COCHIN GUWAHATI HYDERABAD JALANDHAR KOLKATA LUCKNOW MUMBAI PATNA RANCHI NEW DELHI

3 Published by : UNIVERSITY SCIENCE PRESS (An Imprint of Laxmi Publications Pvt. Ltd.) 113, Golden House, Daryaganj, New Delhi Phone : Fax : info@laxmipublications.com Copyright 2011 by Laxmi Publications Pvt. Ltd. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher. Price : Only. First Edition : 2011 OFFICES Bangalore Chennai Cochin , Guwahati , Hyderabad Jalandhar Kolkata Lucknow Mumbai , Patna Ranchi UDF DIGITAL FUND & APP-CHA C 15885/08/05 Typeset at : Kalyani Computer Services, New Delhi. Printed at : Sanjeev Offset Press, Delhi.

4 Dedicated to our parents Late Achintya Kumar Chanda Mrs. Sumitra Chanda & Mr. Shyamal Kanti Banerjee Mrs. Shefali Banerjee

6 CONTENTS 1. FUNDAMENTAL CONCEPTS AND LOGIC GATES Fundamental Concepts Digital Signals Logic Circuits... 2 Review Questions BOOLEAN ALGEBRA Boolean Addition and Multiplication Logic Expressions Rules and Laws of Boolean Algebra Demorgan s Theorems NAND Gate as a Universal Gate NOR Gate as a Universal Gate Boolean Expressions for Gate Networks Sum-of-Products Form Product-of-sums Form Review Questions NUMBER SYSTEMS AND CODES Decimal Numbers Binary Numbers Octal Numbers Hexadecimal Numbers Complements Binary to Decimal Conversion Octal to Decimal Conversion Octal to Binary Conversion (vii)

7 (viii) 3.9 Binary to Octal Conversion Hexadecimal to Decimal Conversion Hexadecimal to Binary Conversion Binary to Hexadecimal Conversion Decimal to Binary Conversion Decimal to Octal Conversion Decimal to Hexadecimal Conversion Binary Arithmetic s and 2 s Complements Digital Codes Review Questions COMBINATIONAL LOGIC DESIGN Introduction Standard Representations for Logical Functions The Karnaugh Map Representation of Logical Functions Representation of Truth Table on Karnaugh Map Representation of Standard Sum of Products Form on Karnaugh Map Representation of Standard Product of Sums Form on Karnaugh Map Simplified Form of Logical Functions using Karnaugh Map Minimization of Logical Functions Specified in Minterms/ Maxterms or Truth Table Using Karnaugh Map Don't Care Conditions Quine McCluskey Minimization Technique Arithmetic Circuits Review Questions FUNCTION OF COMBINATIONAL LOGIC CIRCUITS Multiplexer Combinational Logic Design Using Multiplexers Available Multiplexer ICs Pinout Diagram of Multiplexer Tree

8 (ix) 5.6 Demultiplexers The Decoder Review Questions FLIP-FLOP Introduction Flip-Flops A One Bit Memory Cell Types of Flip-Flops Excitation Table of Flip-Flop Conversion from One Type of Flip-Flop to Another Type of Flip-Flop Applications of Flip-Flops Review Questions COUNTERS Asynchronous (or Ripple) Counters Modulus of the Counter Synchronous (or Parallel) Counters Synchronous Down Counter Design Steps of Synchronous Counter Up/Down Synchronous Counters Review Questions SHIFT REGISTERS Introduction Serial-In Serial-Out (SISO) Shift Registers Serial-In Parallel-Out (SIPO) Shift Registers Parallel-In Serial-Out (PISO) Shift Registers Parallel-In Parallel-Out (PIPO) Shift Register Bidirectional Shift Registers Shift Register Counters Review Questions

9 (x) 9. FINITE STATE MACHINES Introduction Classification of Sequential Circuits Model Classification of Sequential Logic Circuits Clocked Sequential Circuit Design Procedure for Designing Sequential Circuits Review Questions OPERATIONAL AMPLIFIER Circuit Symbol of an Op-Amp Characteristics of an Op-Amp Equivalent Circuit of an Op-Amp Some Applications of Op-Amp Pinout Diagram of a µa 741 IC Op-Amp Review Questions D/A AND A/D CONVERSION Introduction Digital-to-Analog Converters Specifications of D/A Converters An Example of D/A Converter Analog-to-Digital Converters Specifications of A/D Converters An Example of A/D Converter Review Questions PROGRAMMABLE LOGIC DEVICES AND MEMORY Introduction Notations for PLD Programmable Read Only Memory (PROM) Programmable Logic Array (PLA) Programmable Array Logic (PAL) Registered PAL Configurable PAL Generic Array Logic (GAL)

10 (xi) 12.9 Complex Programmable Logic Devices (CPLDs) Field Programmable Gate Array (FPGA) Conclusion Review Questions LOGIC FAMILIES Introduction Characteristics of Digital ICs Resistor-Transistor Logic (RTL) Diode Transistor Logic (DTL) Transistor Transistor Logic (TTL) or (T 2 L) Emitter Coupled Logic (ECL) MOS Logic Complementary MOS Logic (CMOS) Bi-CMOS Logic Circuits Comparison of Different Logic Families Interfacing Review Questions APPENDICES Appendix A Appendix B Appendix C Appendix D Appendix E Appendix F QUESTION SETS INDEX

12 PREFACE A well established and an exciting field, Electrical Engineering broadly involves working with various electronic devices ranging from pocket calculators to super computers. One of the most important reasons for the unprecedented growth of digital electronics is advent of integrated circuits; in fact digital systems have invaded all works of life. Digital logic is concerned with the interconnection of digital components and modules and is a term used to denote the design and an analysis of digital system. Its ever increasing applications have resulted in development the wonder chip the microprocessor, which has been the most fantastic development due to complex digital functions. KEY FEATURES The text not only lays strong emphasis of basic principal but also incorporate topics and contents with advanced concepts. A careful selection of the text material and worked out examples (simple to more complex) enable the students to have in depth knowledge about digital circuits and design aspects and its application. This book also provides various methods and techniques suitable for variety of digital system design application. This book has been written utilizing the long experience of the authors in teaching profession. The major highlights of this book can be summarized as: The subject has been presented in the graded manner and contents a detailed exposition of the fundamentals. Description of the classical methods of design technique. Clearly illustrated worked out example. Step by step and simple problem solving technique enable the students to sharpen their problem solving skills. CHAPTER ORGANISATION This book is divided into thirteen chapters. Each chapter begins with the introduction and ends with questions and problems. Clear diagram and different graded examples have (xiii)

13 (xiv) been provided for all the topics and simple language has been used throughout the book to facilitate understanding of the concept and enable the readers to design digital circuits efficiently. This book can be used by the UG students of any engineering colleges and universities, and those who will be appearing for different competitive examination such as GATE, AMIE, IAS, IES, different state and central level recruitment examination, UPSC, PSC, railway board etc. The authors are greatly thankful to all the staff and management of Bengal Engineering and Science University, Shibpur, Howrah and Dr B C Roy Engineering College, Durgapur, West Bengal for their encouragement and providing necessary facilities to complete the manuscript of the book. The authors highly acknowledge Professor (Dr) Abhijit Chakrabarti for his constant inspiration and advice for publishing this book. The authors also appreciate the patience and inspiration provided by their family members such as Gopa Chanda, Shampa Banerjee, Sayonsom Chanda, Soumyadeep Banerjee, Souptik Banerjee, Swarnadeep Saha. Constructive criticism and/or comments about the book are always welcome. AUTHORS

14 CHAPTER 1 UNDAMENTAL CONCEPTS AND LOGIC GATES 1.1. FUNDAMENTAL CONCEPTS Digital electronics began in 1946 with an electronic digital computer called ENIAC, which was implemented with vacuum-tube circuits. The concept of the digital computer can be traced to Charles Babbage, who developed a mechanical computation device in the 1830s. The first digital computer was built in 1944 at Harvard University, but it was electromechanical, not electronic. All of us are familiar with the impact of modern digital computers, calculators, watches, etc., on their daily life. The main causes of this revolution is the advent of Integrated Circuits (IC), which became possible because of the tremendous progress in semiconductor technology in recent years. The operation of digital computers, calculators, watches etc., and many other systems, are based on the principles of digital techniques and these systems are referred to as digital systems. The term digital is derived from the way in which computers perform operations by counting digits. Initially, applications of digital electronics were confined to computer systems. Today, digital techniques are applied in many diverse areas, such as data processing, process control, military systems, radar, navigation etc. Digital technology has progressed from vacuum-tube circuits to integrated circuits and microprocessors. In an electronic calculator, the input is given with the help of switches. This is converted into electrical signals which have only two discrete values or levels. One of these may be called as LOW level and the other one as HIGH level. The signal will always be of one of the two levels. The actual value of the signal is immaterial as long as it is within the specified range of LOW or HIGH level. This type of signal is known as a digital signal and the circuits inside the calculator used to process these signals are known as digital circuits. So, a calculator is an example of a digital system. 1

15 2 DIGITAL UNDAMENTALS AND APPLICATIONS Digital electronics involves circuits and systems in which there are only two possible states that are typically represented by voltage levels. Other circuit conditions, such as current levels, open or closed switches, and on or off lamps, can also represent the two states. In digital systems, the two states are used to represent numbers, symbols, alphabetic characters, and other types of information. In the two-state number system, called binary, the two digits are 0 and 1. These binary digits are called bits DIGITAL SIGNALS A digital signal has two discrete levels or values. Two different representations of digital signals are shown in ig ig (a) Positive logic and (b) Negative logic system In ig. 1.1(a), higher of the two levels has been designated as HIGH level and the lower as LOW level. This is positive logic system, on the other hand in ig. 1.1(b), higher of the two levels has been designated as LOW level and the lower as HIGH level. This is negative logic system. Any voltage in the range of 3.5 to 5V will be considered as HIGH level in the positive logic system and LOW level in the negative logic system. Similarly, any voltage in the range of 0 to 1V will be considered as LOW level in the positive logic system and HIGH level in the negative logic system. Unless otherwise specified, we shall be dealing with positive logic system LOGIC CIRCUITS Logic circuits is a digital circuit, a switching circuit, or any kind of two-state circuit that duplicates mental processes. The Gate is a digital circuit with one or more input voltages but only one output voltage. Logic gates are the building blocks of digital circuits. They are essential for the physical realization of Boolean expression. The OR, AND and NOT gates can be built using different types of switching elements. The two other gate

Publications ISBN : 9789380856575 Author : Dr.C.

16 Digital Fundamentals and Applications by Dr.C.K Chanda & Sumit Banerjee 40% OFF Publisher : Laxmi Publications ISBN : Author : Dr.C.K Chanda & Sumit Banerjee Type the URL : Get this ebook

DIGITAL SYSTEM DESIGN UNIT I (2 MARKS)

DIGITAL SYSTEM DESIGN UNIT I (2 MARKS) 1. Convert Binary number (111101100) 2 to Octal equivalent. 2. Convert Binary (1101100010011011) 2 to Hexadecimal equivalent. 3. Simplify the following Boolean function