IEEE 754 Floating Point Converter

IEEE 754 is the standard that defines how computers store floating point numbers. A value is split into a sign bit, a biased exponent and a mantissa, giving half, single and double precision formats.

0.1 has no finite binary fraction, so it is rounded to the nearest value the format can hold. This tool shows the stored value and the exact rounding error, which is why 0.1 plus 0.2 is not exactly 0.3.

Single precision uses 32 bits (8 exponent, 23 mantissa) for about 7 decimal digits. Double precision uses 64 bits (11 exponent, 52 mantissa) for about 15 to 17 digits. Half uses 16 bits for low precision storage.

The stored exponent is the real exponent plus a bias: 127 for single, 1023 for double and 15 for half. So a stored exponent field of 128 in single precision means a real exponent of 1.

When the exponent field is all zeros the number is zero or subnormal, filling the gap near zero. When it is all ones the value is Infinity (mantissa zero) or NaN (mantissa non-zero). The tool labels each case.

Yes, it uses round to nearest, ties to even, the IEEE 754 default. The encoder is computed with exact integer math so the bits match what your CPU produces.