Decimal, Binary, Octal, And Hexadecimal number systems.

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

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

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

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.

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

Connection of all number system

Decimal, Binary, Octal, And Hexadecimal number systems.

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