Basetobase

Basetobase is a term used to describe the set of processes, algorithms, and tools that convert representations of numbers or data from one numeral base to another. It encompasses mathematical base conversion as well as broader data representation transformations that rely on different digit sets or encoding schemes. In practice, basetobase refers to both the theory of base conversion and its implementation in software and hardware.

The core idea is to transform a value expressed in a source base B1 into an equivalent value in a target base B2. A common approach is to convert first to an intermediate representation, often base 10 or base 2, and then to the destination base. For integers, the division-remainder method is frequently used, repeatedly dividing by B2 and collecting remainders. For fractional parts, multiplication by the target base and extraction of integer portions provide the digits of the fractional expansion. Some systems use direct conversion algorithms that operate entirely within the two bases without an explicit intermediate step.

Applications of basetobase include calculators, programming language libraries, data encoding schemes, and digital electronics where numbers or data must be represented in different bases for processing or transmission. Examples include converting binary 1011 to decimal 11 or decimal 255 to hexadecimal FF. Limitations arise with very large numbers, bases beyond 36 requiring extended digit sets, non-integer values, and precision or rounding issues in finite representations.

See also numeral system, base conversion, encoding, and numeral representation.