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]
NoteAll 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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