In mathematics, the base (or radix) of a numeral system is the number of distinct digits or symbols, including zero, that a system uses to represent numbers. It also defines how positional value works, where the value of each digit in a number is determined by multiplying it by the base raised to the power of its position.
- Example: In the base-10 system (also known as the decimal system), there are 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The value of each digit depends on its position, with each position representing a power of 10.
- Examples of Common Bases:
- Base-10 (Decimal): Uses digits 0-9, with place values as powers of 10.
- Base-2 (Binary): Uses digits 0 and 1, with place values as powers of 2.
- Base-16 (Hexadecimal): Uses digits 0-9 and letters A-F (for values 10-15), with place values as powers of 16.
The base determines how numbers are constructed and influences arithmetic operations like addition, subtraction, multiplication, and division within that numeral system.