Category: Number System

Base of Number System | Types of Number System

Base of Number System-

 

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

 

Example-01:

 

Consider base 10 Number system which is popularly called as Decimal Number System

  • Since it has base = 10, so total number of digits used in the decimal number system are 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]

 

Example-02:

 

Consider base 2 Number system which is popularly called as Binary Number System

  • Since it has base = 2, so total number of digits used in the binary number system are 2.
  • These digits are-

0 , 1

  • These digits clearly lie in the range [0 , base-1] = [0 , 1]

 

Note

All the digits of any number system with base ‘b’ are always less than ‘b’ as 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-

 

 

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)

 

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