Hexadecimal to decimal

Expanding a hexadecimal integer

Read a hexadecimal whole number as an exact decimal integer. Use this direction when a debugging trace, memory map or specification shows a whole number with hex digits and you want its familiar decimal value. You may enter FF or 0xFF; upper- and lowercase A through F have equal value. The prefix is a clue to the base and does not add to the number.

Each hex digit is weighted by a power of sixteen; the optional 0x prefix identifies the base. Each digit is weighted by a power of sixteen: in FF, the first F is fifteen times sixteen and the second F is fifteen, totaling 255. The result is an exact integer even for values beyond JavaScript’s safe floating-point integer range because the tool uses BigInt. A leading minus sign stays mathematical; no fixed-width signed decoding is performed. For a concrete check, the example input 0xFF produces 255. Keep the original beside the result when comparing it with another application.

What a number base changes

Decimal, binary and hexadecimal are different written forms of the same integer. Decimal has ten digits, binary has two, and hexadecimal has sixteen symbols, adding A through F after 0 through 9. The value itself does not change when its notation changes. A bit is a binary digit; four bits correspond to one hexadecimal digit, which makes hex compact for memory addresses, bit masks and debugging. Use these converters when a specification, log or programming language displays a number in a base other than the one you are reading.

Reading signs and widths correctly

The sign is written separately; these results are not fixed-width two’s-complement machine integers. These converters work with whole integers and retain arbitrary precision through BigInt, so a long value does not silently lose low bits as an ordinary floating-point number might. A leading minus sign represents a negative mathematical integer. It is not a fixed-width two’s-complement byte pattern: the bit string for minus one depends on whether a machine uses eight, sixteen, thirty-two or another number of bits. Add a width and encoding rule separately if a protocol requires one. Do not confuse the binary value of an integer with UTF-8 binary bytes of the characters used to spell it.