Hex to Decimal Converter with Two's Complement

Hex to decimal, decimal to hex, binary and octal in one place

This number base converter shows the same integer in binary, octal, decimal and hexadecimal side by side, plus one custom base of your choice from 2 to 36. Type into any field and all the others update as you type, so hex to decimal, decimal to hex, binary to decimal and decimal to binary are all the same action. Everything is calculated in your browser.

Input is forgiving in the ways real-world values need. A 0x, 0b or 0o prefix is understood in any field — paste 0xFF into the decimal box and it is read as hex, giving 255 — and spaces or underscores used as digit separators (1111_0000, FF FF) are ignored. Letters are case-insensitive, and a leading minus sign works for negative numbers. If you type a digit that does not exist in that base, such as 9 in octal or G in hex, the error names the digit and lists the ones allowed.

All arithmetic uses JavaScript BigInt, so there is no upper limit and no silent rounding. Ordinary converters built on regular JavaScript numbers lose precision above 2^53 (9,007,199,254,740,992), which means a 64-bit ID or hash pasted into them comes back subtly wrong. Here a 128-bit or 256-bit value converts exactly. Binary output can be grouped in fours and hex in pairs to make long values readable, and every field has a copy button.

Signed values and two's complement

Computers store negative integers in two's complement: the bit pattern for -x is what you get by inverting every bit of x and adding one, within a fixed width. That is why -1 as an 8-bit value is 11111111 (hex FF), and why the same byte FF reads as 255 when treated as unsigned and -1 when treated as signed.

The two's complement panel shows the bit pattern of the current value in 8, 16, 32 or 64 bits, along with both readings of that pattern — signed and unsigned — and the hex form. Enter -1 with 32 bits selected and you see FFFFFFFF; enter 4294967295 and you see the same pattern with a signed value of -1. That makes it quick to decode a register dump, check how a C int8_t or Java byte will overflow, or work out what a negative number looks like on the wire. Values outside the chosen width, such as 256 in 8 bits, are reported as out of range rather than silently wrapped.

Limitations and custom bases

Only whole numbers are converted. Fractional values like 0.1 or 3.75 are rejected with a message instead of being truncated, because fractions often have no finite representation in another base (0.1 in binary repeats forever) and silently rounding them would give a misleading answer.

The custom base field covers any radix from 2 to 36 using the digits 0–9 followed by the letters A–Z, the same convention used by JavaScript's parseInt and toString, Python's int(x, base) and most other languages. Base 36 is handy for short IDs; base 32 and base 3 come up in puzzles and coursework. Note that base 32 here means plain positional notation, not the RFC 4648 Base32 encoding, which uses a different alphabet.