The term radix is another word for base in a numeral system. It refers to the number of distinct digits or symbols, including zero, used to represent numbers within that system. The radix determines the positional value of digits in a number, where each position is associated with a power of the radix.
- Radix (or Base): The foundation of a numeral system, indicating how many different symbols or digits are available for representing numbers.
Examples of Radix in Different Numeral Systems
- Radix 10 (Decimal System):
- Definition: The decimal system has a radix of 10, meaning it uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
- Example: In the number 345, the positional values are based on powers of 10.
- Radix 2 (Binary System):
- Definition: The binary system has a radix of 2, using only 0 and 1 to represent numbers.
- Example: In the binary number 1011, the positional values are powers of 2.
- Radix 16 (Hexadecimal System):
- Definition: The hexadecimal system has a radix of 16, using 16 symbols: 0-9 and A-F (where A = 10, B = 11, …, F = 15).
- Example: In the hexadecimal number 2F4, the positional values are based on powers of 16.
Key Concept of Radix
In any numeral system, the value of a number is calculated by multiplying each digit by the radix raised to the power corresponding to its position. The radix influences how numbers are structured, calculated, and converted from one system to another.
Where n is the radix (base) and d₀, d₁, d₂, … are the digits.
Conclusion
Radix is a fundamental concept in numeral systems that defines the structure and operation of numbers within a system. Understanding the radix allows us to perform calculations, convert between numeral systems, and comprehend how different systems like binary, decimal, and hexadecimal function.