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The document outlines different types of number systems, including Binary (Base-2), Octal (Base-8), Decimal (Base-10), and Hexadecimal (Base-16), each defined by its unique base and digits. It explains the characteristics of each system, such as the binary system's use in computers and the decimal system's commonality in daily life. Additionally, it provides examples of how numbers are represented and calculated in each system.

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20 views4 pages

Comp Project

The document outlines different types of number systems, including Binary (Base-2), Octal (Base-8), Decimal (Base-10), and Hexadecimal (Base-16), each defined by its unique base and digits. It explains the characteristics of each system, such as the binary system's use in computers and the decimal system's commonality in daily life. Additionally, it provides examples of how numbers are represented and calculated in each system.

Uploaded by

gamingfreak0517
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Different Types of Number Systems

Number systems are methods of representing numbers in


different ways. The most common types of number
systems are:
• Binary Number System (Base-2)
• Octal Number System (Base-8)
• Decimal Number System (Base-10)
• Hexadecimal Number System (Base-16)
Each number system has its own base, which determines
the number of digits used in the system.

What is the Base of a Number System?


The base of a number system is the number of unique
digits (including zero) used in that system. For example: In
the Binary Number System, the base is 2, and it uses only
two digits: 0 and 1. In the Decimal Number System, the
base is 10, and it uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
The base determines how numbers are represented and
calculated in a system. For example, in the decimal system,
the number 10 represents “ten” because it is a base-10
system.
Characteristics of Binary, Octal, Decimal, and
Hexadecimal Number Systems
Binary Number System
Base: 2
Digits Used: 0 and 1
Characteristics: It is the simplest number system and is
used in computers and digital systems because it
represents two states: ON (1) and OFF (0). Each digit in a
binary number is called a bit. Example: The binary number
1011 represents: [ 1 x 23 + 0 x 22 + 1 x 21+ 1 x 20 = 8 + 0 +
2 + 1 = 11 (in decimal) ]
Octal Number System
Base: 8
Digits Used: 0, 1, 2, 3, 4, 5, 6, 7
Characteristics: It is often used in computing as a
shorthand for binary numbers because one octal digit can
represent three binary digits. Example: The octal number
74 represents: [ 7 x 81 + 4 x 80 = 56 + 4 = 60 (in decimal) ]
Decimal Number System
Base: 10
Digits Used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Characteristics: It is the most commonly used number
system in daily life. Each position in a decimal number
represents a power of 10. Example: The decimal number
345 represents: [ 3 x 102 + 4 x 101 + 5 x 100 = 300 + 40 +
5 = 345 (in decimal) ]
Hexadecimal Number System
Base: 16
Digits Used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Here, A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15 in
decimal.
Characteristics: It is widely used in computing and
programming because it can represent large binary
numbers in a compact form. One hexadecimal digit can
represent four binary digits. Example: The hexadecimal
number 2F represents: [ 2 x 161 + 15 x 160 = 32 + 15 = 47
(in decimal) ]
Summary Table of Number Systems

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