This is a great post! The setup could be clearer: I found it a little difficult to follow (during “a real number x … this value which I will denote f … treat the 31-bit value as an unsigned integer u”) what each of the named variables was intended to refer to, and formatting the 31-bit number as 32 bits threw me off too. Nothing insurmountable but I could feel my brain stumbling before I got to the clever part.