Learning Digital Electronics (Extract)

Learning Digital Electronics This book is a practical guide to digital electronics, covering the essential components of modern digital systems: number systems, logic gates, Boolean algebra, combinational and sequential logic, and more.

Through more than 20 structured projects, you’ll design and build digital systems using real-world components such as logic gates, multiplexers, decoders, flip-flops, counters, and shift registers. The projects range from basic LED logic circuits to digital locks, display systems, traffic light controllers, and timing-based designs.

Selected projects introduce the use of tools such as CircuitVerse for circuit simulation, while several designs make use of 74HC-series logic devices, commonly used in digital hardware prototyping.

Inside, you’ll find:

> Clear coverage of number systems and binary arithmetic > Logic gate fundamentals and universal gate implementations > Step-by-step projects using flip-flops, counters, and registers > Real-world design with 74HC-series logic chips > Techniques for designing combinational and sequential systems

Prof Dr Dogan Ibrahim holds a BSc degree in Electronic Engineering, an MSc degree in Automatic Control Engineering, and a PhD in Digital Signal Processing.

He worked in numerous industrial organizations before returning to academic life.

Prof. Ibrahim is the author of over 60 technical books and over 200 technical articles on microcontrollers, microprocessors, and related fields. He is a Chartered Electrical Engineer and a Fellow of the Institution of Engineering and Technology.

This book takes a design-first, application-driven approach to digital electronics—built around working circuits, tested logic, and hands-on experimentation.

Elektor International Media www.elektor.com

Learning Digital Electronics • Dogan Ibrahim

With 20+ Practical Projects in Logic and Circuit Design

Learning Digital Electronics With 20+ Practical Projects in Logic and Circuit Design

Academy Pro Title by

Dogan Ibrahim

SKUXXXXX_COV_Learning Digital Electronics.indd Alle pagina's

02-10-2025 15:44

Learning Digital Electronics With 20+ Practical Projects in Logic and Circuit Design

● Dogan Ibrahim

● This is an Elektor Publication. Elektor is the media brand of Elektor International Media B.V.

PO Box 11, NL-6114-ZG Susteren, The Netherlands Phone: +31 46 4389444

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● Declaration

The material in this publication is of the nature of general comment only, and does not represent professional advice. It is not intended to provide specific guidance for particular circumstances and it should not be relied on as the basis for any decision to take action or not take action on any matter which it covers. Readers should obtain professional advice where appropriate, before making any such decision. To the maximum extent permitted by law, the author and publisher disclaim all responsibility and liability to any person, arising directly or indirectly from any person taking or not taking action based on the information in this publication.

● I SBN 978-3-89576-700-5 Print ISBN 978-3-89576-701-2

eBook

● © Copyright 2025 Elektor International Media www.elektor.com

Editor: Glaucileine Vieira

Elektor is the world's leading source of essential technical information and electronics products for pro engineers, electronics designers, and the companies seeking to engage them. Each day, our international team develops and delivers high-quality content - via a variety of media channels (including magazines, video, digital media, and social media) in several languages - relating to electronics design and DIY electronics. www.elektormagazine.com

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Contents

Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter 1 • Number Systems and Base Conversions . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Number Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Number System Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Signed Binary Numbers, 1’s Complement, 2’s Complement, Signed Magnitude . . . 14 1.5 Binary Coded Decimal (BCD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Chapter 2 • Logic Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 AND Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 OR Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 NOT Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.5 Exclusive-OR Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.6 Exclusive-NOR Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.7 Universal Logic Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.7.1 NAND gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.7.2 NOR gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Chapter 3 • Logic Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2 Classification of Logic Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2.1 Unipolar Logic Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2.2 Bipolar logic families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3 The 74HC Logic Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.4 Project 1 – AND Gate with LED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.5 Using a Digital Software Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.5.1 Using CircuitVerse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.6 Some 74HC Logic Device Pin Layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Chapter 4 • Boolean Algebra and Logic Minimization . . . . . . . . . . . . . . . . . . . . . . . 31 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 Laws of Boolean Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.3 Minimization of Logic Expressions – Karnaugh Maps . . . . . . . . . . . . . . . . . . . . . . 31 4.4 Using Universal Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.4.1 Using NAND gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.4.2 Using NOR gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.4.3 Project 2 – Pushbutton-operated digital lock . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.5 Multi-outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Chapter 5 • Combinational Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.2 Majority Logic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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Learning Digital Electronics

5.3 Project 3 – 3-Input Majority Logic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.4 Project 4 – Half-Adder Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.4.1 Simulation of the half-adder circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.5 Full-Adder Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.5.1 Simulation of the full adder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.6 Project 5 – 2-Input Multiplexer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.7 Project 6 – Dark Reminder – 2-Input Multiplexer . . . . . . . . . . . . . . . . . . . . . . . . 55 5.8 74HC Multiplexer Chip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.8.1 74HC157 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.9 Project 7 – Demultiplexers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.10 74HC Decoder Chip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.11 Project 8 - 2-to-4 Binary Decoder - Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.12 Project 9 - 7-Segment Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Chapter 6 • SR Flip-Flops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 6.2 SR Flip-Flop from NAND Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 6.3 Project 10 – Burglar Alarm Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6.4 Project 11 – Entry-Exit System Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.5 Positive-Triggered NAND Gate SR Flip-Flop . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 6.6 SR Flip-Flop from NOR Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 6.7 Gated SR Flip-Flop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Chapter 7 Other Flip-Flops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 7.2 D-type Flip-Flop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 7.3 JK Flip-Flop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 7.4 T Flip-Flop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.5 D Flip-Flop from JK Flip-Flop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.6 T Flip-Flop from D Flip-Flop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.7 T Flip-Flop from JK Flip-Flop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Chapter 8 • Digital Counters, Shift Registers, Oscillators, and Others . . . . . . . . . . 79 8.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 8.2 Project 12 – 4-Bit Binary Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 8.3 Project 13 – Modulo-10 Binary Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 8.4 Projet 14 – Traffic Lights Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 8.5 Cascaing 74HC161 Counter Chips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 8.6 Timed Sequential Event Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 8.7 Project 15 – Alternately Flashing LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 8.8 Project 16 – Morse Code Key Exerciser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 8.9 Project 17 – 4-bit Shift Register – Chasing Lights . . . . . . . . . . . . . . . . . . . . . . . . 94 8.10 Project 18 – 8-bit Shift Register Package – Chasing Lights . . . . . . . . . . . . . . . . . 95 8.11 Project 19 – 8-bit Shift Register Package – Chasing Lights – Only One Light ON . . 98 8.12 Project 20 – Faster-Finger-First with Two Players . . . . . . . . . . . . . . . . . . . . . . 100 8.13 Project 21 – Digital Dice with LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

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Contents

Chapter 9 • Clocked Synchronous Sequential Logic Circuit Design . . . . . . . . . . . 107 9.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 9.2 The Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 9.3 Flip-Flop Excitation Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 9.4 Project 22 – Design of a Modulo-4 Binary Up Counter . . . . . . . . . . . . . . . . . . . . 108 9.5 Designing a Modulo-4 Binary Down Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 9.6 Designing a Modulo-5 Binary Up Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 9.7 Designing a Modulo-3 Binary Up/Down Counter . . . . . . . . . . . . . . . . . . . . . . . . 115 9.8 Designing a Ring Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 9.8 Sequence Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Chapter 10 • Components Used in Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

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Learning Digital Electronics

Preface The world around us is becoming increasingly digital. From the smartphones in our hands to the embedded systems controlling industrial processes, digital electronics form the backbone of modern technology. At the heart of this transformation lies a fundamental toolkit—logic gates and sequential logic systems. This book is written for students, hobbyists, and engineers who wish to gain a clear, practical understanding of how these systems are designed, built, and applied.

This book is not merely an introduction to digital electronics. It walks through the core ideas of digital logic, aiming to build solid knowledge and support hands-on skills. The focus is on understanding through design: each chapter progresses logically from theory to application, with carefully crafted examples and projects that highlight real-world relevance.

The first part of the book introduces basic concepts such as binary systems, Boolean algebra, and the operation of individual logic gates. From there, we move into combinational logic— including multiplexers, decoders, and adders—and eventually transition into sequential systems, including flip-flops, counters, registers, and state machines.

The real strength of digital systems lies in their ability to remember and react over time, and this is where sequential logic becomes key. Designing these systems requires both creative thinking and analytical precision. In this book, readers will learn how to design and build systems that operate synchronously and asynchronously. Special attention is given to design methodology, helping readers learn how to think in terms of states, transitions, and control logic.

What sets this book apart is its project-based approach. Each major topic is reinforced through hands-on exercises and practical design challenges—from simple binary counters to more complex systems. These projects are intended not just to reinforce learning but also to encourage experimentation, critical thinking, and creativity.

I wrote this book with a deep appreciation for both the elegance and utility of digital design.

Whether you’re an undergraduate student exploring this field for the first time, a selftaught enthusiast, or a professional looking to refresh your knowledge, my goal is to make these concepts both accessible and engaging.

You are encouraged to read with curiosity and build with confidence. The most effective learning happens when theory meets practice—when you wire up your first circuit, troubleshoot a misbehaving flip-flop, or see a state machine operate exactly as intended.

Through this book, I hope to bridge the gap between understanding and application, and to equip you with the tools to explore digital systems on your own.

I hope this book is a useful step in your journey into digital electronics. Let’s get started.

Dogan Ibrahim 2025, London

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Chapter 1 • Number Systems and Base Conversions

Chapter 1 • Number Systems and Base Conversions 1.1 Overview Digital systems use various number systems such as Decimal, Binary, Octal, and Hexadecimal.

For example, the hexadecimal number system is commonly used in microcontroller-based applications. In this chapter, we will learn the commonly used number systems, and also learn how to convert from one number system to another system.

1.2 Number Systems Table 1.1 shows the commonly used number systems from decimal 0 to decimal 15.

Decimal (base 10)

Binary (base 2)

Octal

Hexadecimal

(base 8)

(base 16)

00

0000

00

0

01

0001

01

1

02

0010

02

2

03

0011

03

3

04

0100

04

4

05

0101

05

5

06

0110

06

6

07

0111

07

7

08

1000

10

8

09

1001

11

9

10

1010

12

A

11

1011

13

B

12

1100

14

C

13

1101

15

D

14

1110

16

E

15

1111

17

F

Table 1.1 Number systems Decimal number system: This is a base-10 number system used in everyday counting and calculations. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit is a power of 10, e.g., 100, 101, 102, 103, etc. For example, the decimal number 2518 has the following digits: 2518 = 2 x 103 + 5 x 102 + 1 x 101 + 8 x 100

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Learning Digital Electronics

Binary number system: This is a base-2 number system used in digital electronics. It uses two digits: 0 and 1. Each digit is a power of 2, e.g., 20, 21, 22, 23, etc. For example, the binary number 00101011 has the following digits: 00101011 = 0 x 27 + 0 x 26 + 1 x 25 + 0 x 24 + 1 x 23 + 0 x 21 + 1 x 20 Octal number system: This is a base-8 number system used in digital electronics. It uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each digit is a power of 8, e.g., 80, 81, 82, 83, etc. For example, the octal number 2317 has the following digits: 2317 = 2 x 83 + 3 x 82 + 1 x 81 + 7 x 80 Hexadecimal number system: This is a base-16 number system commonly used in microcontroller and digital logic applications. It uses 16 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Each digit is a power of 16, e.g., 160, 161, 162, 163, etc. For example, the hexadecimal number A1B2 has the following digits: A1B2 = 10 x 163 + 1 x 162 + 11 x 161 + 2 x 160

1.3 Number System Conversions Decimal to binary conversion The steps are: • Divide the decimal number by 2.

• Record the remainder (0 or 1).

• Continue dividing the quotient by 2 until the quotient is 0.

• The binary equivalent is the remainders read from bottom to top For example, let us convert the decimal number 41 to binary.

Integer quotient Remainder 41 ÷ 2 20 ÷ 2 10 ÷ 2 5 ÷ 2 2 ÷ 2 1 ÷ 2

20 10 5 2 1 0

1 0 0 1 0 1

Therefore, the answer is, reading from bottom to top: 101001

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Chapter 1 • Number Systems and Base Conversions

Binary to decimal conversion The steps are: • Write down the binary number.

• Multiply each digit (0 or 1) by 2 raised to the power of its position, starting from 20 at the rightmost digit.

• Add the result of all the multiplications.

• The sum is the decimal equivalent.

For example, let us convert the binary number 01101001 into decimal Decimal = 0 x 27 + 1 x 26 + 1 x 25 + 0 x 24 + 1 x 23 + 0 x 22 + 0 x 21 + 1 x 20 = 105 Decimal to octal conversion The steps are: • Divide the decimal number by 8.

• Record the remainder (from 0 to 7).

• Continue dividing the quotient by 8 until the quotient becomes 0.

• The octal equivalent is the remainders read from bottom to top.

For example, let us convert the decimal number 285 to octal.

Integer

quotient Remainder

285÷8 35÷8 4÷8

35 4 0

5 3 4

Therefore, the answer is, reading from bottom to top is: 435 Octal to decimal conversion The steps are: • Write down the octal number.

• Multiply each digit by 8 raised to the power of its position, starting from 80 at the rightmost digit.

• Add the result of the multiplications.

• The sum is the decimal equivalent.

For example, let us convert the octal number 271 into decimal.

Decimal = 2 x 82 + 7 x 81 + 1 x 80 = 185

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Learning Digital Electronics

Decimal to hexadecimal conversion The steps are: • Divide the decimal number by 16.

• Record the remainder (0-9 or A-F).

• Continue dividing the quotient by 16 until the quotient becomes 0.

• The hexadecimal equivalent is the remainders read from bottom to top.

For example, let us convert the decimal number 2481 to hexadecimal.

Integer

quotient Remainder

2481÷16 155÷16 9÷16

155 9 0

1 11 (B) 9

Therefore, the hexadecimal equivalent of 2481 is, reading from bottom to top: 9B1 Hexadecimal to decimal conversion The steps are: • Write down the hexadecimal number.

• Multiply each digit by 16 raised to the power of its position, starting from 160 at the rightmost digit.

• Add the results of the multiplications.

• The sum is the decimal equivalent.

For example, let us convert the hexadecimal number A1B2 into decimal.

Decimal = 10 x 163 + 1 x 162 + 11 x 161 + 2 x 160 = 40960 + 256 + 176 + 2 = 41394 Hexadecimal to binary conversion The steps are: • Each hexadecimal number corresponds to a 4-bit binary number.

• Write the 4-bit binary number corresponding to each hexadecimal digit.

For example, let us convert the hexadecimal number AB12 to binary.

A 1010

B 1011

1 0001

2 0010

Therefore, the binary number is: 1010101100010010.

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Chapter 1 • Number Systems and Base Conversions

Binary to hexadecimal number conversion The steps are: • Each 4-bit binary numbers correspond to a hexadecimal digit • Divide the binary numbers into groups of 4 bits starting from the rightmost bit • If the number of bits is not a multiple of 4, add leading zeroes to the leftmost group • Write the equivalent hexadecimal digit for each 4-bit group For example, let us convert the binary number 1001110001100001 to hexadecimal.

1001 9

1100 C

0110 6

0001 1

Therefore, the hexadecimal number is 9C61 Octal to binary conversion The steps are: • Each octal number corresponds to a 3-bit binary number • Write the 3-bit binary number corresponding for each octal digit.

For example, let us convert the octal number 277 to binary.

2 010

7 111

7 111

Therefore, the binary number is 010111111.

Binary to octal conversion The steps are: • Each 3-bit binary group correspond to an octal digit • Divide the binary numbers into groups of 3 bits starting from the rightmost bit • If the number of bits is not a multiple of 3, add leading zeroes to the leftmost group • Write the equivalent octal number for each group For example, let us convert the binary number 111101101 to octal.

111 7

101 5

101 5

Therefore, the octal number is 755.

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Learning Digital Electronics

1.4 Signed Binary Numbers, 1’s Complement, 2’s Complement, Signed Magnitude Both signed and unsigned numbers are represented by a string of bits on a digital computer.

It is up to the user to determine whether a number is positive or negative. If the binary number is signed, then the leftmost bit represents the sign. A zero represents that the number is positive, while a one represents that the number is negative. For example, the number 01001 can be considered as an unsigned or a positive signed number since the most significant bit is zero. The number 11001 represents the binary number 25 when considered as an unsigned number, or -9 when considered as a signed number since the top bit is negative.

The representation of signed numbers in the last example is known as the signed magnitude format. Here, the number consists of a magnitude with the most significant bit representing the sign of the number. When arithmetic operations are performed on a digital computer, negative numbers are represented using the 2’s complement notation.

This is done by complementing each bit of the number (known as 1’s complement) and then adding one to the number. Some examples are given below by considering the decimal number 9, assuming 8-bit representation: Signed magnitude format:

00001001

+9

Signed magnitude format:

10001001

-9

1’s complement: 11110110 2’s complement: 11110111

-9

Using the 2’s complement notation, arithmetic operations can easily be done with binary numbers.

1.5 Binary Coded Decimal (BCD) This is a commonly used encoding system where each decimal digit is represented by 4 bits ranging from 0 to 9. BCD is used in calculators and clocks where decimal displays are required. Some examples of BCD numbers are given here.

Let us consider the decimal number 3467. This is represented in BCD format as follows: 3 0011

4 0100

6 0110

7 0111

Therefore, the BCD representation of decimal number 3467 is 0011 0100 0110 0111.

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Chapter 2 • Logic Gates

Chapter 2 • Logic Gates 2.1 Overview Logic gates are the fundamental building blocks of digital electronics. They operate on one or more digital input signals to produce a digital output signal. Logic circuits respond to two distinct voltage levels at their inputs, which represent logic 0 or logic 1.

For example, a particular digital system may operate at +5 volts, where any voltage lower than 2 volts may represent logic 0 and any voltage higher than 3 volts may represent logic 1. As shown in Figure 2.1, the voltage range and its logical equivalent have an acceptable range. The intermediate region (here between 2 volts and 3 volts) is only crossed during a state transition, and no input or output remains in this transition region.

Figure 2.1 Digital voltage levels for the example In this chapter, you will learn the input-output relationships (known as Truth Tables) for commonly used logic gates.

2.2 AND Gate The AND gate can have two, three or more inputs and one output. The output state of the AND gate is logic 1 if all its inputs are at logic 1, otherwise, the output state is 0 if any of its inputs is 0. Figure 2.2 shows the logic diagram of a two input AND gate and its Truth Table.

Assuming the inputs are A and B and the output is Y, the AND gate input-output relationship

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Learning Digital Electronics

is represented using one of the following notations. In this book we will use the notation without any symbols between the gate inputs: Y = A.B or

Y = A and B

or

Y=A&B

or

Y = AB (preferred)

Figure 2.2 Two-input AND gate

2.3 OR Gate The OR gate can have two, three, or more inputs and one output. The output state of the OR gate is logic 1 if at least one of its inputs is at logic 1, otherwise, the output state is 0 if all its inputs are 0. Figure 2.3 shows the logic diagram of a two input OR gate and its Truth Table. Assuming inputs are A and B and the output is Y, the OR gate input-output relationship is represented using one of the following notations: Y = A or B or Y = A | B or Y = A+B (preferred)

Figure 2.3 Two input OR gate

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Chapter 2 • Logic Gates

2.4 NOT Gate The NOT gate has one input and one output. It is also known as an inverter or an inverting buffer. When the input signal is 0, the output is 1 and vice versa. Figure 2.4 shows the logic diagram and the truth table of a NOT gate. Assuming the input is A and the output is Y, the NOT gate input-output relationship is represented using one of the following notations: Y = NOT A or Y = A’ or Y = Sometimes a bar is placed on top of the input as shown in the figure.

Figure 2.4 NOT gate

2.5 Exclusive-OR Gate The Exclusive-OR gate (also called the XOR gate) is commonly used to perform modulo additions in digital circuits. This gate has two inputs and one output. The output is logic 0 if both inputs are the same; otherwise, the output is logic 1. Figure 2.5 shows the logic diagram and truth table of the XOR gate. Assuming the inputs are A and B and the output is C, the XOR gate input-output relationship is represented using one of the following notations.

C = A XOR B or C = A’B + AB’ or C= 𝐴 ⊕ 𝐵

Sometimes a small circle with a + symbol inside is used to denote an XOR gate as shown in the Figure.

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Learning Digital Electronics

Figure 2.5 Exclusive-OR gate

2.6 Exclusive-NOR Gate The Exclusive-NOR gate (also called the XNOR gate) has two inputs and one output. The output is logic 1 if both inputs are the same; otherwise, the output is logic 0. Figure 2.6 shows the logic diagram and truth table of the XNOR gate. Assuming the inputs are A and B and the output is Y, the XNOR gate input-output relationship is represented using one of the following notations.

Y = A XNOR B

or

Y = AB + A’B’

or

Y=A⊙B

Sometimes a small circle with a dot symbol inside is used to denote an XNOR gate.

Figure 2.6 Exclusive-NOR gate

2.7 Universal Logic Gates Any digital logic expression can be realised by using two types of gates: the NAND gate and the NOR gate. These gates are also known as the universal logic gates. You will learn in later chapters how to realize logic circuits using these universal logic gates.

2.7.1 NAND gate The NAND gate is a combination of an AND gate followed by a NOT gate. It can have two or more inputs and a single output. The output of a NAND gate is 1 when either of its inputs is 1 or both of its inputs are 0. Figure 2.7 shows the logic diagram of a two-input NAND gate and its truth table. Assuming A and B are the inputs and Y is the output of a NAND gate, the input-output relationship is represented using one of the following notations: Y = (AB)’ or Y = A NAND B or Y =

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Chapter 2 • Logic Gates

Figure 2.7 NAND gate

2.7.2 NOR gate The NOR gate is a combination of an OR gate followed by a NOT gate. It can have two or more inputs and a single output. The output of a NOR gate is 1 when all of its inputs are 0.

Figure 2.8 shows the logic diagram of a two-input NOR gate and its truth table. Assuming A and B are the inputs and Y is the output of a NOR gate, the input-output relationship is represented using one of the following notations: Y = (A+B)’

or

Y = A NOR B or

Y=

Figure 2.8 NOR gate

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Learning Digital Electronics

Index A AND gate Astable calculator Astable timer B Binary coded decimal Binary counter Binary decoder Binary number system Binary to decimal conversion Binary to hexadecimal conversion Binary to octal conversion Bipolar logic Boolean algebra Burglar alarm C Chasing lights CircuitVerse CMOS Combinational logic

15, 25 75 74

14 79 62 10 11 13 13 21 31 68

98 27 20 43

D Dark reminder Decimal number system Decimal to binary conversion Decimal to hexadecimal Decimal to octal conversion D flip flop Demultiplexer Decoder Digital dice Digital lock DTL

55 9 10 12 11 73 59 61 103 37 21

E ECL Entry-exit system Exclusive NOR gate Exclusive OR gate

22 70 18 17

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F Fan out Faster finger first Flashing LEDs Full adder

23 100 89 50

G Gated SR flip flop

72

H Half adder Hexadecimal number system Hexadecimal to binary conversion Hexadecimal to decimal conversion

46 10 12 12

J JK flip flop

76

K Karnaugh maps

31

L Laws of Boolean algebra LDR

31 55

M Majority logic Modulo 3 binary up down counter Modulo 4 binary down counter Modulo 4 binary up counter Modulo 5 binary up counter Modulo 10 binary counter Morse code exerciser Multi outputs Multiplexer

43 115 111 108 113 83 92 41 52

N NAND gate NMOS NOR gate NOT gate Number systems

18, 36 20 19, 37 17 9

Index

O Octal number system Octal to decimal conversion Octal to binary conversion OR gate

10 11 13 16

P PMOS Positive triggered SR flip flop

20 71

R Ring counter RTL

118 21

S Schottky TTL Seven segment display Sequence detector Shift register Signed binary numbers Signed magnitude Software simulator SR flip flops Synchronous sequential logic

22 63 121 94 14 14 27 67 107

T T flip flop Traffic lights controller TTL

77 85 21

U Universal logic gate

18, 36

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Learning Digital Electronics This book is a practical guide to digital electronics, covering the essential components of modern digital systems: number systems, logic gates, Boolean algebra, combinational and sequential logic, and more.

Through more than 20 structured projects, you’ll design and build digital systems using real-world components such as logic gates, multiplexers, decoders, flip-flops, counters, and shift registers. The projects range from basic LED logic circuits to digital locks, display systems, traffic light controllers, and timing-based designs.

Selected projects introduce the use of tools such as CircuitVerse for circuit simulation, while several designs make use of 74HC-series logic devices, commonly used in digital hardware prototyping.

Inside, you’ll find:

> Clear coverage of number systems and binary arithmetic > Logic gate fundamentals and universal gate implementations > Step-by-step projects using flip-flops, counters, and registers > Real-world design with 74HC-series logic chips > Techniques for designing combinational and sequential systems

Prof Dr Dogan Ibrahim holds a BSc degree in Electronic Engineering, an MSc degree in Automatic Control Engineering, and a PhD in Digital Signal Processing.

He worked in numerous industrial organizations before returning to academic life.

Prof. Ibrahim is the author of over 60 technical books and over 200 technical articles on microcontrollers, microprocessors, and related fields. He is a Chartered Electrical Engineer and a Fellow of the Institution of Engineering and Technology.

This book takes a design-first, application-driven approach to digital electronics—built around working circuits, tested logic, and hands-on experimentation.

Elektor International Media www.elektor.com

Learning Digital Electronics • Dogan Ibrahim

With 20+ Practical Projects in Logic and Circuit Design

Learning Digital Electronics With 20+ Practical Projects in Logic and Circuit Design

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Dogan Ibrahim

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02-10-2025 15:44