Decode a Float

The leftmost bit of any positive binary number is always 1. So if you were to left-justify a positive binary number, the top bit would always be 1. If the top bit is always 1, there is no need to implement it. Floating point numbers use this trick.

You can determine the bits of an integer using only arithmetic operations by repeatedly dividing by two and collecting the remainders. Today’s puzzle is to determine the bits of a floating point number using only arithmetic operations (no decode-float or integer-decode-float).