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Nan-box IEEE 754 encodes 32-bit floating points with 1 bit for the sign, 8 bits for the exponent, and 23 bits for the number part (mantissa). For the specific case of NaN (e.g. the result of dividing 0 by 0, or the square root of a negative number), the spec encodes this as 11111111 in the exponent. The sign and the mantissa can be anything, and the spec suggests this can be used for "diagnostic information". One/some of these bits is/are commonly used to indicate a quiet NaN (qNaN) which could be expected vs. a signaling NaN (sNaN) which could be unexpected and should trigger an halting exception. This behavior is however sometimes different on different hardware.