# Conversion of Number Systems

Topics: Binary numeral system, Hexadecimal, Decimal Pages: 50 (7277 words) Published: February 11, 2013
THE PROJECT ON
CONVERSION OF NUMBER SYSTEMS

INDEX Sr no.| TOPIC| Pg No| 1.| Title| 1|
2.| Subtitle| 1|
3.| Abstract| 2|
4.| Introduction| 3|
| 4.1| Decimal System| 5|
| 4.2| Binary System| 6|
| 4.4| Octal system| 8|
5.| Algorithms| 9|
6.| Solved Examples| 14|
7.| Programs| 18|
9.| Applications| 37|
10.| References| 37|
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TITLE: CONVERSION OF NUMBER SYSTEMS
SUBTITLE:
1. Conversion of binary to decimal number system
2. Conversion of octal to decimal number system
3. Conversion of hexadecimal to decimal number system
4. Conversion of decimal to binary number system
5. Conversion of decimal to octal number system
6. Conversion of decimal to hexadecimal number system
7. Conversion of octal to hexadecimal number system
8. Conversion of octal to binary number system
9. Conversion of hexadecimal to octal number system
10. Conversion of hexadecimal to binary number system
11. Conversion of binary to octal number system
12. Conversion of binary to hexadecimal number system

ABSTRACT
The number is a symbol or a word used to represent a numeral, while a system is a functionally related groups of elements, so as whole, a number is set or group of symbols to represent numbers or numerals. In other words, any system that is used for naming or representing numbers is a number system. We are quite familiar with decimal number system using ten digits. However digital devices and computers use binary number system instead of decimal number system, having only two digits i.e 0 and 1. Binary number system is based on the same fundamental concept of decimal number system. Various other number systems also use the same fundamental concept of decimal number system e.g. octal number system(using 8 digits) and hexadecimal number systems(using 16 digits). The knowledge of number systems, their limitations, data formats, inter-conversion and other related terms is essential for understanding of computers and successful programming for digital devices. Understanding all these number systems and particularly their inter conversion of number systems requires a lot of time and a large number of techniques to expertise. The well known number systems and their inter conversions to be discussed are binary, octal, decimal and hexadecimal.

INTRODUCTION
The study of number systems is useful to the student of computing due to the fact that number systems other than the familiar decimal (base 10) number system are used in the computer field. Digital computers internally use the binary (base 2) number system to represent data and perform arithmetic calculations. The binary number system is very efficient for computers, but not for humans. Representing even relatively small numbers with the binary system requires working with long strings of ones and zeroes. The hexadecimal (base 16) number system (often called "hex" for short) provides us with a shorthand method of working with binary numbers. One digit in hex corresponds to four binary digits (bits), so the internal representation of one byte can be represented either by eight binary digits or two hexadecimal digits. Less commonly used is the octal (base 8) number system, where one digit in octal corresponds to three binary digits (bits). In the event that a computer user (programmer, operator, end user, etc.) needs to examine a display of the internal representation of computer data (such a display is called a "dump"), viewing the data in a "shorthand" representation (such as hex or octal) is less tedious than viewing the data in binary representation. The binary, hexadecimal , and octal number systems will be looked at in the following pages. The decimal number system that we are all familiar with...