To determine the significand of an IEEE-754 32-bit binary floating-point value:
Figure out where the leading (most significant) 1 bit is. That is the starting point. Calculate 23 more bits. If there is anything left over, round it into last of the 24 bits (carrying as necessary).
Exception: If the leading bit is less than 2-126, use the 2-126 bit as the starting point, even though it is zero.
That gives the mathematical significand. To get the bits for the significand field, remove the first bit. (And, if the exception was used, set the encoded exponent to zero instead of the normal value.)
Another exception: If the leading bit, after rounding, is 2128 or greater, the conversion overflows. Set the result to infinity.