Base of Number System | Types of Number System

Base of Number System-

 

  • Base of a number system is the total number of digits used in that number system.
  • Number system with base ‘b’ has its digits in the range [0 , b-1].
  • It is also called as radix of a number system.

 

Examples-

 

Consider the following examples-

 

Base 10 Number System-

 

Consider base 10 number system popularly called as decimal number system-

  • Total number of digits used in this number system are 10 since it has base 10.
  • These digits are 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9.
  • These digits clearly lie in the range [0 , base-1] = [0 , 9].

 

Base 2 Number System-

 

Consider base 2 number system popularly called as binary number system-

  • Total number of digits used in this number system are 2 since it has base 2.
  • These digits are 0 and 1.
  • These digits clearly lie in the range [0 , base-1] = [0 , 1].

 

Important Note-

 

It is important to note that-

  • All the digits of any number system with base ‘b’ are always less than ‘b’.
  • This is clear from the range [0 , base-1] in which the digits of any number system lie.

 

Types of Number System-

 

Four most commonly used number systems are-

 

 

  1. Decimal Number System
  2. Binary Number System
  3. Octal Number System
  4. Hexadecimal Number System

 

The following table shows the base and digits used in these number systems-

 

Number SystemBaseDigits Used
Decimal Number System100, 1, 2, 3, 4, 5, 6, 7, 8, 9

(Total 10 digits)

Binary Number System20, 1

(Total 2 digits)

Octal Number System80, 1, 2, 3, 4, 5, 6, 7

(Total 8 digits)

Hexadecimal Number System160, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

(Total 16 digits)

 

To gain better understanding about Basics of Number System,

Watch this Video Lecture

 

Next Article- Converting Any Base to Base 10

 

Get more notes and other study material of Number System.

Watch video lectures by visiting our YouTube channel LearnVidFun.

Summary
Base of Number System | Types of Number Systems
Article Name
Base of Number System | Types of Number Systems
Description
Base of a Number System is the total number of digits used in that number system. Types of Number Systems- Decimal Number System, Binary Number System, Octal Number System, Hexadecimal Number System.
Author
Publisher Name
Gate Vidyalay
Publisher Logo
Liked this article? Share it with your friends and classmates now-