positsioonarvusüsteem

Positsioonarvusüsteem is a numeral system where the value of a digit depends on its position within the number. In a positional system, each digit has a face value, and its position determines a power of the base. For example, in the decimal system (base-10), the number 123 means (1 * 10^2) + (2 * 10^1) + (3 * 10^0). This is in contrast to non-positional systems, such as Roman numerals, where the value of a numeral is fixed regardless of its position (e.g., in XVI, X is always 10, V is 5, and I is 1, irrespective of their order).

The most common positional system is the base-10 decimal system, which uses ten digits (0 through 9). However, other bases are also used. The binary system (base-2) uses only two digits (0 and 1) and is fundamental to computer science. The hexadecimal system (base-16) uses sixteen digits (0-9 and A-F) and is often used in computing for representing memory addresses and color codes.

The concept of a positional system relies on the existence of a zero digit to represent the absence of a value in a particular position. Without zero, distinguishing between numbers like 12, 102, and 120 would be impossible in a purely positional notation. Positional numeral systems greatly simplify arithmetic operations like addition, subtraction, multiplication, and division compared to non-positional systems.