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Avinash Bhagat, Lovely Professional University Unit 1: Number Systems

Unit 1: Number Systems Notes

CONTENTS
Objectives
Introduction
1.1 Decimal Number System
1.2 Binary Number System
1.3 Hexadecimal Number System
1.4 Octal Number System
1.5 Conversion from One Number System to Another
1.5.1 Converting from Another Base to Decimal
1.5.2 Converting from Decimal to Another Base (Division-Remainder Technique)
1.5.3 Converting from a Base Other Than 10 to Another Base Other Than 10
1.5.4 Short-cut Method for Binary to Octal Conversion
1.5.5 Short-cut Method for Octal to Binary Conversion
1.5.6 Short-cut Method for Binary to Hexadecimal Conversion
1.5.7 Short-cut Method for Hexadecimal to Binary Conversion
1.6 Summary
1.7 Keywords
1.8 Review Questions
1.9 Further Reading

Objectives

After studying this unit, you will be able to:
• Discuss the decimal number system
• Explain about binary number system
• Discuss the hexadecimal number system
• Discuss the octal number system
• Understand the method of conversion from one number system to another

Introduction

We are familiar with the decimal number system in which digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
The computer uses binary digits for its operation. In the binary system there are only two digits
0 and 1. The programmer feeds instruction and data in alphabets and decimal digits. But for the
operation of the computer these are converted to binary bits. This chapter deals with the conversion
of binary numbers to decimal numbers and vice versa. It also deals with hexadecimal and octal
system. Computer circuitry is usually designed to process hexadecimal or octal number.
Number Systems are two types:
1. Non-Positional Number System
2. Positional Number System

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