Rangdom

See how a float is really stored

IEEE 754 stores a real number as three fields: a single sign bit, a biased exponent (11 bits for binary64, 8 for binary32), and a mantissa or fraction (52 / 23 bits). Type a decimal like 0.1 or -2.5e-3 and the exact stored value reveals the rounding error — entering 0.1 in 64-bit shows the number actually held is 0.1000000000000000055511151231257827021181583404541015625, which is why 0.1 + 0.2 never quite equals 0.3.

Switch the direction to paste a hex encoding (with or without the 0x prefix) and decode it back into a number, bits, and fields. The classification line names the value as Normal, Subnormal, Zero (including −0), Infinity, or NaN. Only binary64 and binary32 are covered; half precision, bfloat16, and 80-bit extended formats are out of scope.