Digital Electronics 1

Combinational Logic Circuits

Tertulien Ndjountche

• Publisher: Wiley-ISTE
• Year: 2016
• Print ISBN: 9781848219847
• eBook ISBN: 9781119318637
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Energy

The omnipresence of electronic devices in our everyday lives has been accompanied by the downscaling of chip feature sizes and the ever increasing complexity of digital circuits.

This book is devoted to the analysis and design of digital circuits, where the signal can assume only two possible logic levels. It deals with the basic principles and concepts of digital electronics. It addresses all aspects of combinational logic and provides a detailed understanding of logic gates that are the basic components in the implementation of circuits used to perform functions and operations of Boolean algebra. Combinational logic circuits are characterized by outputs that depend only on the actual input values.

Efficient techniques to derive logic equations are proposed together with methods of analysis and synthesis of combinational logic circuits. Each chapter is well structured and is supplemented by a selection of solved exercises covering logic design practices.

1
Number Systems

1.1. Introduction

Digital systems are used to process data and to perform calculations in most instrumentation, monitoring and communication devices. As physical quantities and signals can only take discrete values in a digital system, the interpretation of real-world information requires the use of interface circuits such as data converters.

In general, numbers may be represented in different numeration systems. The decimal system is commonly used in routine transactions while the binary system is the basis for digital electronics. Every number (or numeration) system is defined by a base (or radix), which is a collection of distinct symbols. The representation of a number in a numeration system may be considered as a change in base. In a positional number system, a value of a number depends on the place occupied by each of its digits in the representation.

1.2. Decimal numbers

The decimal number system uses the following 10 numbers or symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The radix is thus 10.

EXAMPLE 1.1.– Decompose the numbers 734 and 12345 into powers of 10.

The decomposition of the number 734 takes the form:

For the number 12345, we have:

Depending on its position, each number is multiplied by the appropriate power of 10. The right-most digit represents the unit digit.

1.3. Binary numbers

Binary number system is based on two-level logic, conventionally noted as 0 (low level) and 1 (high level). It is a system with a radix of two.

EXAMPLE 1.2.– Convert the decimal numbers 13 and 125 into binary numbers.

The decomposition of the number 13 in powers of 2 is written as:

For the number 125, we have:

The binary code that is then obtained...

Table of contents

• Cover
• Table of Contents
• Title
• Copyright
• Preface
• 1 Number Systems
• 2 Logic Gates
• 3 Function Blocks of Combinational Logic
• 4 Systematic Methods for the Simplification of Logic Functions
• Bibliography
• Index
• End User License Agreement