Convert number base

Convert Number Base takes an integer written as text, a source base, and a target base, then returns the same integer in the requested numeral system. It supports every base from 2 through 36, so the familiar binary, octal, decimal, and hexadecimal systems work alongside less common compact alphabets. Letters are accepted without regard to case and results use uppercase letters. Before converting, the capability checks every character against the source base and reports invalid input instead of silently producing a misleading value. Its integer arithmetic is exact, deterministic, and suitable for values much longer than ordinary machine integers.

Choose the source base and enter the number

Start by identifying the numeral system in which the original string is written. Binary uses base 2 and therefore permits only zero and one. Octal uses base 8 and permits zero through seven.

Decimal uses base 10, while hexadecimal uses base 16 and adds A through F for values ten through fifteen. The capability extends the same pattern through base 36, where Z represents thirty-five. An optional leading plus or minus sign is allowed, and surrounding whitespace is ignored.

Do not include prefixes such as 0x, 0b, separators, decimal points, commas, or explanatory text; the input represents one whole integer, not a formatted programming-language literal. Letter digits are case-insensitive, so ff and FF mean the same hexadecimal value. Every character is validated before a result is returned.

For example, 102 is rejected in base 2 because the digit two cannot occur there, even though it would be valid in base 3. This strict behavior helps catch a mistaken source base early rather than returning a plausible but incorrect conversion.

Understand how the exact conversion works

A positional numeral is evaluated from left to right. For each digit, the running value is multiplied by the source base and the new digit value is added. This is the same place-value rule taught for decimal numbers, generalized to any radix from two through thirty-six.

After the exact integer value has been recovered, the converter repeatedly divides it by the target base. Each remainder becomes one target digit, and reading those remainders in reverse order produces the final string. The implementation performs those operations with arbitrary-precision integers instead of floating-point numbers, so it does not lose low-order digits when the input exceeds JavaScript's usual safe integer range.

Zero is always returned as 0, including inputs such as -000, because negative zero has no separate integer representation. Leading zeroes are removed naturally from other results, and alphabetic output digits are uppercase for stable comparisons. The algorithm has no network access, random values, clock reads, stored state, or model calls.

Consequently the same fields always yield the same result, making the capability safe for tests, build scripts, data transformations, and reproducible documentation.

Use the result safely in applications

Keep it as text unless you know that the converted value fits exactly in the numeric type used by your application. This matters for long identifiers, bit masks, checksums, database keys, and values handled by languages whose standard number type has a fixed width. A leading minus sign is preserved for nonzero negative integers, while the digits themselves follow the target alphabet 0-9 and A-Z.

Both bases must be integers within the inclusive range from 2 to 36. Handle that error as a validation failure and ask the caller to correct the number or base; do not retry the same request.