positsionaalsüsteem

A positsionaalsüsteem, or positional numeral system, is a method of writing numbers where the value of a digit depends on its position within the number. This is in contrast to non-positional systems, like Roman numerals, where the value of a symbol is fixed regardless of its placement. The most common positional system is the decimal system, also known as base-10. In this system, digits 0 through 9 are used, and each position represents a power of 10. For example, in the number 123, the '1' represents 100 (10^2), the '2' represents 20 (2 * 10^1), and the '3' represents 3 (3 * 10^0).

The concept of a positional system requires a radix or base, which is the number of unique digits used in the system. The base also determines the powers to which it is raised for each position. Binary (base-2) uses only digits 0 and 1, while hexadecimal (base-16) uses digits 0-9 and letters A-F to represent values 10-15. The inclusion of a zero digit is crucial for positional systems to distinguish between numbers like 10, 100, and 1, as it acts as a placeholder. Positional systems are fundamental to modern arithmetic and computation due to their efficiency and the ease with which operations like addition and multiplication can be performed.