Digital. Design. R. Ananda Natarajan B C D

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1 Digital E A B C D Design Y R. Ananda Natarajan

2 Digital Design

3

4 Digital Design R. ANANDA NATARAJAN Professor Department of Electronics and Instrumentation Engineering Pondicherry Engineering College Puducherry Delhi

5 DIGITAL DESIGN R. Ananda Natarajan 2015 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN The export rights of this book are vested solely with the publisher. Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi and Printed by Mohan Makhijani at Rekha Printers Private Limited, New Delhi

6 To My beloved mother Late R. Saraswathi Ramaiah ( )

7

8 Contents Preface xvii Acknowledgements xix 1. Number System 1 52 Learning Objectives Introduction to Digital Systems Decimal Number System Octal Number System Hexadecimal Number System Binary Number System Why Binary Number System is Used in Computers Number Base Conversions Decimal to Binary and Binary to Decimal Conversions Decimal to Octal and Octal to Decimal Conversions Decimal to Hexadecimal and Hexadecimal to Decimal Conversions Need for Octal and Hexadecimal Systems Binary to Hexadecimal and Octal Conversions Complement of a Number (r 1) s Complement of a Number s Complement and 1 s Complement Binary Arithmetic Binary Addition Binary Subtraction Binary Multiplication Binary Division s Complement Subtraction s Complement Subtraction Signed Binary Numbers Signed Binary Addition Signed Binary Subtraction Binary Codes Binary Coded Decimal (BCD) or 8421 Code Code 25 vii

9 viii Contents Code Excess-3 Code Gray Code Advantage of Gray Code Binary Coded Pentary (BCP) Code Alphanumeric Codes Error Detecting and Correcting Codes Parity Code Other Error-Detection Codes Hamming Code 34 Multiple Choice Questions with Answers 36 Solutions to Multiple Choice Questions 38 Short Questions with Answers 40 Review Questions Boolean Algebra Learning Objectives Introduction Fundamental Definitions Inverse Operation or Logical Negation (NOT) Logical AND Operation Logical OR Operation Boolean Postulates and Theorems Truth Table Proof of DeMorgan s First Theorem Using Truth Table (Perfect Induction Method) Proof of DeMorgan s Second Theorem Principle of Duality Consensus Theorem Algebraic Simplifications and Manipulations Transposition Theorem Complement of a Function Minterms and Maxterms Minterms Maxterms Binary Logic Definitions of Binary Logic Electronic Logic Gates NAND Gate NOR Gate Exclusive OR (XOR) Gate Exclusive NOR (XNOR) Gate Preparing Logic Diagrams Extension of Multi-inputs Fanout and Fanin High Impedance State in Gates Buffer Equivalent Circuit Representations 83

10 Contents ix 2.8 Sum of Products (SOP) and Product of Sums (POS) Expressions Sum of Products (SOP) Product of Sums (POS) Standard Form or Canonical Form Logic Design Universal Building Blocks NAND is Universal Building Block NOR is a Universal Building Block Procedure to Convert a Given Logic Circuit in Terms of NAND Gate Implementation Procedure to Realise the Given Logic Expression Using NOR Gate Karnaugh Map Two Variable Karnaugh Map for Sum of Products Form (SOP) Three Variable Karnaugh Map for Sum of Products Form (SOP) Four Variable Karnaugh Map for Sum of Products Form (SOP) Five Variable Karnaugh Map for Sum of Products Form (SOP) Don t Care Combinations Product of Sums Form (POS) Implicant Quine-McCluskey or Tabulation Method of Minimisation of Logic Functions 116 Multiple Choice Questions with Answers 125 Solutions to Multiple Choice Questions 134 Short Questions with Answers 142 Review Questions Arithmetic Circuits Learning Objectives Introduction Steps to Design Arithmetic Circuits Adder Half Adder Full Adder Parallel Adder (Ripple Carry Adder) Subtractor Half Subtractor Full Subtractor Parallel Subtractor One s Complement Generator Adder/Subtractor Propagation Delay in Adders Carry Look Ahead Adder Serial Arithmetic Circuits BCD Adder Binary Multiplier Parallel Multiplier 180 Multiple Choice Questions with Answers 182 Solutions to Multiple Choice Questions 184 Short Questions with Answers 184 Review Questions 188

11 Digital Design 30% OFF Publisher : PHI Learning ISBN : Author : NATARAJAN, R. ANANDA Type the URL : Get this ebook

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