Baseto

Baseto is the operation of converting numbers between numeral bases. In positional numeral systems, the value is represented as a sum of digits times powers of the base. Baseto enables representations across bases such as binary, decimal, and hexadecimal, and is used in computing, data encoding, and mathematics.

Core methods. The standard approach converts the input to an internal big-integer form, then repeatedly divides by the target base, collecting remainders to form the output digits in reverse order. For efficiency with large numbers or bases, algorithms may work in larger chunks or use divide-and-conquer strategies, and some systems allow arbitrary base digits beyond the common 0–9 and A–Z.

Inputs, outputs, and constraints. Proper handling of signs, leading zeros, and invalid digits is essential. Bases are typically restricted to integers greater than 1; error handling must flag invalid bases or digits. Performance depends on input length, base sizes, and the underlying arithmetic implementation.

Applications and implementations. Baseto concepts appear in educational tools, calculators, and programming languages, where converting numbers between bases is common. Many languages provide built-in base conversion utilities; libraries and APIs implementing baseto often emphasize correctness, performance, and support for nonstandard bases or large numbers.

See also. Numeral system, base conversion, big integer arithmetic, encoding schemes.