Introduction to Digital Electronics

J. Crowe,Barrie Hayes-Gill

• Publisher: Butterworth-Heinemann
• Year: 1998
• ISBN:
  9780080534992
• Topic: Design
• Subtopic: Industrial Design

This text takes the student from the very basics of digital electronics to an introduction of state-of-the-art techniques used in the field. It is ideal for any engineering or science student who wishes to study the subject from its basic principles as well as serving as a guide to more advanced topics for readers already familiar with the subject. The coverage is sufficiently in-depth to allow the reader to progress smoothly onto higher level texts.

1

Fundamentals

1.1 INTRODUCTION

This chapter introduces the essential information required for the rest of the book. This includes a description of Boolean algebra, the mathematical language of digital electronics, and the logic gates used to implement Boolean functions. Also covered are the ‘tools’ of digital electronics such as truth tables, timing diagrams and circuit diagrams. Finally, certain concepts such as duality, positive and negative assertion level logic and universal gates, that will be used in later chapters, are introduced.

1.2 BASIC PRINCIPLES

1.2.1 Boolean algebra - an introduction

The algebra of a number system basically describes how to perform arithmetic using the operators of the system acting upon the system’s variables which can take any of the allowed values within that system. Boolean algebra describes the arithmetic of a two-state system and is therefore the mathematical language of digital electronics. The variables in Boolean algebra are represented as symbols (e.g. A, B, C, X, Y etc.) which indicate the state (e.g. voltage in a circuit). In this book this state will be either 0 or 1.¹ Boolean algebra has only three operators: NOT, AND and OR. The symbols representing these operations, their usage and how they are used verbally are all shown in Table 1.1. Note that whereas the AND² and OR operators operate on two or more variables the NOT operator works on a single variable.

Table 1.1

Boolean variables and operators

Example 1.1

A circuit contains two variables (i.e. signals), X and Y, which must be OR’d together. How would this operation be shown using Boolean algebra, and how would you describe it verbally?

Solution

The operation would be spoken as X or Y and written as X + Y.

Example 1.2

The output Y of a logic circuit with two inputs, A and B, is given by the Boolean arithmetic expression,

. How would this be described verbally?

Solution

This would be spoken as either Y equals A and B bar, or alternatively Y equals A and not B.

1.2.2 The three Boolean operators

The basic gates (i.e. circuit elements) available in digital electronics perform the three Boolean algebraic operations of NOT, AND and OR. The symbols for these gates are shown in Fig. 1.1. In order to both design and analyse circuits it is necessary to know the output of these gates for any given inputs.

Fig. 1.1 The three basic Boolean operators

The NOT operator

Since any Boolean variable can only be either 0 or 1 (Boolean algebra is a two- state system) then if it is 0...