A number representation system, also known as a numeral system or numerical notation, refers to a systematic way of expressing numbers using symbols or digits. It encompasses the rules and conventions employed to represent and manipulate numerical quantities.
In a number representation system, each symbol or digit has a specific value that contributes to the overall numeric value of a number. These symbols, typically called numerals, are used to construct all types of numbers, including integers, fractions, and complex numbers. The arrangement and combination of these symbols follow a positional notation, where the value of a symbol depends on its position within the number.
The choice of symbols and the base, or radix, of a number representation system varies across different cultures and mathematical systems. The most widely used number representation system is the decimal system, which employs the digits 0 to 9 and a base of 10. Other common systems are the binary system (base 2), used in digital computers, and the hexadecimal system (base 16), frequently used in computer programming.
Number representation systems facilitate various arithmetic operations, such as addition, subtraction, multiplication, and division. Different systems may have specific algorithms and rules for performing these operations efficiently. Understanding the characteristics and properties of various number representation systems is fundamental in mathematics, computer science, and everyday numerical reasoning.
