Arvoperusta

Arvoperusta is a term used in Estonian to describe the base of a numeral system or the foundational basis for representing numbers. The word combines arv, meaning number, and perusta, meaning base or foundation. In mathematics, an arvoperusta (base) is the integer greater than one that determines the digits available and the place-value structure of a positional numeral system.

In a given base b, the digits must satisfy 0 ≤ d < b, and a number with digits d_k...d_0 represents the value sum d_i · b^i. Common examples include base-10 (decimal), base-2 (binary) and base-16 ( hexadecimal). For instance, the binary numeral 1011_2 equals 11 in decimal, and the hexadecimal numeral 1A3_16 equals civilized 1·256 + 10·16 + 3 = 291 in decimal. Notation often explicitly indicates the base, using subscripts (e.g., 1011_2) or prefixes in informal contexts (e.g., 1A3 in base 16).

Arvoperusta is central in number theory, digital computing, and education, where understanding how place value changes with the base is fundamental. In computing, bases such as binary and hexadecimal are particularly important for data representation, bitwise operations, and memory addressing. The concept also relates to logarithms, where the base of the logarithm specifies the rate at which values grow.

Historically, various numeral bases have been used across cultures, with decimal becoming dominant for everyday arithmetic, while bases like 2 and 16 play pivotal roles in modern computing. See also numeral system, radix, positional notation, and base conversion.