## 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 System Base Digits Used Decimal Number System 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9(Total 10 digits) Binary Number System 2 0, 1(Total 2 digits) Octal Number System 8 0, 1, 2, 3, 4, 5, 6, 7(Total 8 digits) Hexadecimal Number System 16 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F(Total 16 digits)

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