Digital Electronics | Number System And Codes

INTRODUCTION

In this modern world of electronics, the term digital is mostly associated with a computer. Number systems are used to represent data in digital systems. In this chapter, we will consider the following topics:

• Analog and digital system.
• Number systems: decimal, binary, octal, and hexadecimal number systems 
• Counting in various number systems 
• Number system conversions 
• Basic binary arithmetic: addition, subtraction, multiplication, division. 
• Complements of numbers: 1's and 2's complement of binary number, 7's and 8's complement of octal number, 9's and 10's complement of decimal number, 15's and 16's complement of hexadecimal number. 
• Number representation in binary system: sign magnitude representation, 1's complement representation, 2's complement representation.
• Complement binary, octal, decimal, and hexadecimal arithmetic: addition and subtraction using complement of numbers.
• Binary codes: BCD, Excess-3 code, Gray code; their conversion.

Analog and digital systems

There are two types of electronic circuits and systems:

Analog System: Analog systems are those in which physical quantities are represented over a continuous range of values.

Digital System: Digital systems are those in which physical quantities are represented in digital form; that is, the quantities can take on only discrete values.

The comparison between analog and digital system are given in the following text

Advantages of Digital System

1. Digital systems are easier to design.

2. Storage of information is easy.

3. Greater accuracy and precision.

4. Digital systems are less affected by noise.  5.Operation can be controlled by a program.

6. More digital circuitry can be fabricated on integrated circuit (IC) devices.

7. Digital Systems are more reliable.

Limitations of Digital System

In real world, most physical quantities are analog in nature. These quantities are used as input signals of system and monitored for controlling the system. In digital system, these analog quantities are converted to digital quantities. Because of these conversions, the processing time increases and the system becomes more complex.

Number system

A number system is nothing more than a code that uses symbols to represent a number. In general, in any number system, there is an ordered set of symbols known as digits. A number is made up of a collection of digits and it has two parts; integer and fraction, both are separated by a radix point (.). The number is represented as,

 Where, r = radix or base of the number system n= number of digits in the integer part

m = number of digits in fractional part

d_n-1= most significant digit (MSD)

d_-m= least significant digit (LSD) On the basis of number of different symbols used (radix), number systems are classified as

1. Decimal number system

2. Binary number

3.Octal number system

4. Hexadecimal number system

Now, we discuss each number system in following sections.