A numerical system, also known as a number system, is a way of representing numbers using a specific set of symbols. The choice of symbols and rules for their arrangement determine how numbers are written and manipulated. Numerical systems are essential for counting, performing arithmetic operations, and representing quantities in various contexts.
Common numerical systems include:
- Decimal System (Base-10): The most familiar system, where numbers are represented using digits 0-9. Each digit’s position represents a power of 10.
- Binary System (Base-2): Uses digits 0 and 1. Each digit’s position represents a power of 2, commonly used in computers.
- Octal System (Base-8): Uses digits 0-7. Each digit’s position represents a power of 8.
- Hexadecimal System (Base-16): Uses digits 0-9 and letters A-F to represent values. Each digit’s position represents a power of 16.
- Roman Numerals: Uses combinations of letters (I, V, X, L, C, D, M) to represent numbers.
Each numerical system has its own advantages and applications. For example, the binary system is fundamental for digital electronics, while the decimal system is used in everyday life and most calculations. Hexadecimal and octal systems are used for representing memory addresses and working with low-level programming.
Converting between numerical systems involves understanding the place value of each digit and the corresponding powers of the base.