IEEE 754 Converter

An IEEE 754 converter shows how a computer actually stores a floating-point number. Enter a decimal value like 3.14159 and the tool encodes it into the exact bit pattern defined by the IEEE 754 standard, splitting the result into its three parts: the sign bit, the exponent field, and the mantissa (also called the fraction or significand). It works in both directions, so you can also paste a 32-bit or 64-bit binary string, or its hexadecimal equivalent, and decode it back into the number it represents.

Floating-point numbers are not stored the way we write them. A value is kept as a sign, a power of two, and a fractional significand, following the scheme in IEEE 754-2019. That design is why 0.1 plus 0.2 does not equal exactly 0.3, why some decimals round when stored, and why very large and very small magnitudes are possible in the same 32 or 64 bits. Seeing the sign, exponent, and mantissa laid out makes these behaviours concrete instead of mysterious, which is invaluable when you are debugging a numeric bug, writing a serializer, studying computer architecture, or comparing single and double precision.

This tool runs 100% in your browser and uses the same ArrayBuffer and DataView primitives the JavaScript engine uses internally, so the bit patterns match what your CPU would produce, down to the rounding. Single precision (binary32) uses 1 sign bit, 8 exponent bits, and 23 mantissa bits; double precision (binary64) uses 1 sign bit, 11 exponent bits, and 52 mantissa bits. The special cases are handled too: positive and negative zero, subnormal numbers, infinity, and NaN are each identified. Nothing you enter is uploaded, and the tool keeps working offline once loaded.