This document discusses various number systems: decimal, binary, octal, and hexadecimal, highlighting their definitions, historical context, and applications. Each system is described in terms of its number range, uses in computing, and conversion methods to and from other systems. The document emphasizes the importance of these systems in arithmetic and digital technology.

2. Name : AOUN ABBAS
ROLL # 19012510-050
COURSE: : MSC

3. TOPIC
 Decimal,
 Binary,
 Octal, Hexadecimal number systems

4. Contents:
Introduction
Define number system
Decimal system
Binary system
Octal system
Hexadecimal system

5. Introduction
 what is number system ?
• Its used to define a set of values which show some
quantity about any thing.
• A number system can be represented differently in
different system.
• Not only for computers but also imp- for arithmetic
work.

6. Symbols

7. History
Roman numbers systems :
• Developed by ancients roman around 5,000 years B.C.
• Roman number based on seven symbols.
I = 1, V= 5, X= 10, L= 50, C= 100, D= 500, M= 1000

8. History :
 Arabic number system:
• These numbers developed by al-Khwarizmi and
alkindi around 12th century.

10. Binary number system
 This system include only one and zero digits.
 Every value is represented by 1 & 0 symbols.
 Its is also known base 2 number system.
 Example : (010)2 = 2

11. Applications
• In computers all data represents in binary & for
arithmetic process.
• Many integrated circuits used them in logic gates.
• It is used in all digital devices

12. Decimal number system
• This system include only ten digits from 0 to 9.
• Its also known base 10 number system.
• 0 is minimum value & 9 is maximum value digit.
• Examples : 10 = in this digit 0 is at unit and 1 at
ten position

13. Applications
• Use in daily routine use for different work.
• its easy to use for arithmetic purpose.

14. Octal number system
• This system number include eight number from 0
to 7.
(0,1,2,3,4,5,6,7)
• Its also known base 8 number system.
• Example:
(273)8

15. Applications
• Scientists are often looking for shortcut to do
things by using this number system.
programing
• Is was very popular in PDP/-8 and old computer
systems.

16. Hexadecimal number system
• It contains 16 digits from 1 to 9 and 6 letters from A to F.
A = 11 , B = 12, C = 13, D = 14, F =15,
• This also known as base 16 number system.
• Example: (273)8

17. Applications
• It’s used in computer system for
representation of colores.
• Hexadecimal provide shortcut method for
apply binary numbers

18. CONVERSION

19. Conversion of binary number system
 Binary to Decimal :
(1010) binary = 10 decimal

20. Conversion of decimal number system
 Decimal to binary number system :
Decimal 35 = 0100101 Binary
 LSD ?
 MSD ?

21. CONVERSION OF OCTAL NUMBER SYSTEM
 Conversion of Octal to Decimal :
(𝟏𝟒𝟑) 𝟖 octal = (𝟗𝟗) 𝟏𝟎 Decimal

22. Conversion of hexadecimal
 Hexadecimal to decimal number system :
(𝑨𝟐𝑭𝟕) 𝟏𝟔 Hexadeciam = (𝟒𝟏𝟕𝟏𝟗) 𝟏𝟎

23. Connection of all number system