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Number Base Converter

Convert numbers between binary, octal, decimal, hex and any base.

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Questions
How large a number can this handle?
Arbitrarily large. Conversion uses BigInt, so values well beyond 64 bits convert exactly rather than losing precision the way floating-point arithmetic would.
Why does hex show up everywhere in programming?
Because one hex digit is exactly four bits, so a byte is always two digits and bit patterns stay readable. Octal has a similar property with three bits and survives mainly in Unix file permissions.