Binary / Hexadecimal / Decimal Converter
Enter a value in any field to instantly convert it to the other two number systems.
Formulas
Decimal → Binary: Repeatedly divide the decimal number by 2; collect remainders in reverse order.
N = dn·2n + … + d1·21 + d0·20
Decimal → Hexadecimal: Repeatedly divide by 16; map remainders 10–15 to A–F.
N = hn·16n + … + h1·161 + h0·160
Binary → Hexadecimal: Group binary digits into nibbles (4 bits) from the right; convert each nibble to its hex digit.
1111 11112 = FF16 = 25510
Assumptions & References
- Supports arbitrarily large integers via JavaScript
BigInt. - Negative decimal values are converted using a sign-magnitude representation (a leading minus sign), not two's complement.
- Binary input may optionally be prefixed with
0b; hexadecimal input may optionally be prefixed with0x. - Hexadecimal letters are displayed in uppercase (A–F).
- Fractional (floating-point) numbers are not supported; integers only.
- Reference: IEEE 1541 standard for binary prefixes; NIST SP 330 for SI units.