The document discusses various number systems, including binary, decimal, octal, and hexadecimal, highlighting their histories, structures, and applications. Each system serves distinct purposes in fields such as computer science, finance, and engineering. Number systems are essential for effective data representation and problem-solving in mathematics and everyday life.

1. NUMBER SYSTEM
AND CONVERSION
PRESENTED BY:
KRISH SHRESTHA
ADARSH BISTA
NABIN BAM

2. Acknowledgement
Computer Department
Mr Dhirendra Fauzdar
ECA Department
Mr Jay Gaudel

3. History
Introduction
Comparison
Types of Number System
Applications
Conclusion
Table Of Contents

4. History
 The concept of a number system has
evolved over time, and it doesn't
have a single inventor.
 Different cultures and civilizations
contributed to the development of
various number systems.

5. Introduction to Number System
• Number systems form a fundamental concept in
mathematics offering symbols and rules for
representing and manipulating quantities.
• Number systems are comprised of a set of
symbols that are used to represent different
numerical values.
• Specific rules dictate how symbols combine to
represent numbers.
• Different systems (e.g., decimal, binary) cater to
diverse mathematical needs.

6. Comparison of Number Systems
Number system Base Digits Application
Binary 2 0-1 computer system, digital
electronics
Decimal 10 0-9 Computer programming,
mathematics
Octal 8 0-7 File permission and
networking
Hexadecimal 16 0-9 and A-F Colour representation
and memory addressing

7. 1. Data Representation in Computers
2. Memory Management
3. Networking and Communication
4. Cryptography
5. Education and Understanding
6. Problem Solving
Importance

8. Binary Number
System
• The binary number system is a
base-2 number system that
uses only two digits: 0 and 1.
• Each 0 or 1 is a 'bit' (binary
digit).

9. Uses of Binary
Number System
• Computers
• Digital Electronics
• Telecommunications
• Internet

10. Decimal Number
System
• It uses ten digits (0-9) for representing
numbers.
• Separates whole numbers from fractions
in a decimal.
• Decimal numbers can be positive,
negative or zero.
• Also known as the base-10 system.
• Most commonly used in everyday life.

11. Uses of Decimal Number
System
• Main system for counting and math
operations.
• Used in banking and accounting for
financial transactions.
• Applied in measurements such as
length, weight, and volume.
• Represents time, temperature, and
practical quantities.

12. Octal Number
System
• Octal is a base-8 number system
using digits 0-7.
• Commonly used in computer
programming to represent and handle
binary data.
• Octal numbers denote file permissions
for owner, group, and others.

13. Uses of Octal Number
System
• File Permissions
• Unix Timestamp
• Digital Electronics
• Networking
• Machine Code

14. Hexadecimal Number
System
• Hexadecimal (hex) is a base-16 number
system.
• Uses 0-9 and A-F
• Widely used in computing and digital
systems.
• A-F represent 10-15
• Used for memory addresses machine
instructions

15. Uses of Hexadecimal
Number System
• Binary Data Handling
• Color Codes
• Memory Addresses

16. Applications of Number System
Computer Science Engineering Finance
Statistics Medicine

17. Conclusion
• Number systems are the building blocks of math.
• Used in daily life, science, technology, and engineering.
• Essential for logical thinking, problem-solving, and data
interpretation.
• Used in coding, finance, physics, and cryptography.

18. References
• https://www.splashlearn.com/math-vocabulary/number-sense/number-
system
• https://www.geeksforgeeks.org/what-is-a-number-system/