baseY

baseY refers to a numeral system with base Y, where Y is an integer greater than 1. In such a system, each digit represents a value from 0 to Y−1, and the value of a multi-digit numeral is obtained by multiplying each digit by successive powers of Y and summing the results. The base is typically indicated by a subscript, as in (d_k d_{k−1} ... d_0)_Y, though in informal notes the base may be stated verbally.

Digit symbols often follow a conventional set: 0 through 9 for values 0–9, and letters A, B, C, etc., for values 10 and above, up to the limit where a single character Suffices. For bases larger than 36, extended symbol sets or multi-character tokens are used, since a single alphanumeric character is no longer sufficient to represent all digits.

Common examples illustrate the idea: in base 2, the numeral 1011_2 equals decimal 11_10; in base 16, 2F_16 equals decimal 47_10. Converting between bases typically involves either repeated division (to obtain digits in the target base) or repeated multiplication (to build the target base representation from decimal). Arithmetic in baseY follows the same rules as decimal arithmetic, with carries occurring when a sum or product reaches Y.

Applications of baseY include computer science and digital electronics, where binary (base 2), octal (base 8), and hexadecimal (base 16) are common. It also serves in education to illustrate positional notation and number representations in non-decimal bases. Limitations include the lack of standard digit sets for very large bases and the need for custom encoding in programming environments. See also numeral system, base conversion, binary, octal, decimal, and hexadecimal.