lol... you don't need this formula. what you need to know is, that a float is also just represented by some bytes in the memory. what is relevant to you in this article is this part: http://en.wikipedia...._representation as you can see, an 8byte float uses 51 bits for the mantissa and 11 for the exponent. but whether those bytes are interpreted as a float or as an integer is irrelevant to the process of writing it to a file.
since GML can only write bytes to a binary file, you would need to cut the float (called real in GM) into 8 pieces and write them manually. to get the internal representation of the real bytewise, you would need the pointer, but GML cannot handle pointers.
so, it's just not possible, because the purpose of GML is to create games, not to write a database handler. this is the reason why GML can use DLLs. no language is an "Inspector Gadget". Write your binary file I/O in another language and make a DLL of it, or use a common DLL like suggested. if you just want to learn the how-to in some language, get the Demo of PureBasic and write a little program for file I/O.