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.
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].
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-
- Decimal Number System
- Binary Number System
- Octal Number System
- Hexadecimal Number System
The following table shows the base and digits used in these number systems-
|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)
To gain better understanding about Basics of Number System,
Next Article- Converting Any Base to Base 10
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