Digital Logic Techniques

John Stonham

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351454995
• Edition: 3
• Topic: Technologie et ingénierie
• Subtopic: Ingénierie de l'électricité et des télécommunications

The third edition of Digital Logic Techniques provides a clear and comprehensive treatment of the representation of data, operations on data, combinational logic design, sequential logic, computer architecture, and practical digital circuits. A wealth of exercises and worked examples in each chapter give students valuable experience in applying the concepts and techniques discussed.Beginning with an objective comparison between analogue and digital representation of data, the author presents the Boolean algebra framework for digital electronics, develops combinational logic design from first principles, and presents cellular logic as an alternative structure more relevant than canonical forms to VLSI implementation. He then addresses sequential logic design and develops a strategy for designing finite state machines, giving students a solid foundation for more advanced studies in automata theory.The second half of the book focuses on the digital system as an entity. Here the author examines the implementation of logic systems in programmable hardware, outlines the specification of a system, explores arithmetic processors, and elucidates fault diagnosis. The final chapter examines the electrical properties of logic components, compares the different logic families, and highlights the problems that can arise in constructing practical hardware systems.

Numerical representation of information 1

Objectives

□ To distinguish between analogue and digital quantities.

□ To investigate the binary number system.

□ To define and examine binary-coded decimal numbers.

□ To specify the essential properties of a position sensing code.

□ To introduce the concepts of error detection and correction in binary data.

In almost all activities, we are constantly dealing with quantities or measurements. This information is expressed in the form of numbers and can be processed in a digital system, provided it can be represented in an electronic form.

Information is almost always encoded in binary in a digital system and a wide range of codes exist. The choice of a particular code is influenced by the type of operation to be carried out on the data.

In this chapter, methods of representing numerical data in binary will be introduced. It is essential that the designer is familiar with fundamental coding techniques, as the form in which information is represented has significant influence on the design, performance and reliability of a digital system.

Analogue and digital data

The first step in any data processing operation is to obtain information about the objects or phenomena of interest. The acquisition of information usually involves taking measurements on some property or characteristic of a system under investigation. In order to evaluate and assess the system, the measurements are monitored, scaled, compared, combined, or operated on in various ways. It is therefore essential that we have standard ways of representing our information.

Measurements can be divided into two broad categories. An analogue measurement is continuous and is a function of the parameter being measured. Conversely, a digital quantity is discrete and it can only change by fixed units.

All drips are assumed to be the same size

Figure 1.1 shows two beakers being filled, one from a dripping tap and the other from a trickling tap. The build-up of water in the first beaker is typically digital, as the smallest change in volume is equal to one drip and the value increases in steps. In the second beaker, the volume of water increases continuously with time. It has an analogue property.

Analogue and digital electronic circuits can be devised to process data. Analogue circuits such as operational amplifiers are cheap and powerful, but the analogue approach has two main disadvantages. The real world problem must have a precise electronic model and accurate measurements need to be made on that model.

For details on op-amps, refer to Horrocks, D.H. Feedback circuits and Op-amps (2nd edn, Chapman & Hall, 1990)

In digital electronic circuits, there is no need to make precise time-dependent measurements as a problem is modelled by a set of rules based on logic, which will be developed throughout this book. One major drawback of digital circuits is resolution. If the resolution is increased by reducing the minimum step changes allowed in the parameters, the amount of electronic circuitry must increase.

Fig. 1.1 (a) A digital or discrete system, (b) An analogue or continuous system.

The resolution of a digital system determines the smallest detectable change in its parameters. It is dependent on the number of bits used to represent quantities.

The electronics engineer should be aware that analogue, digital or a hybrid combination of both methods may be relevant to a particular information processing operation. Neither approach should be precluded as any one method may provide a significantly simpler solution to a given problem.

Information is all about numbers. A number is a label with a unique meaning, and the remainder of this chapter will examine ways of representing information.

Exercise 1.1

Which of the following items invol...