Printing bits as IEEE-754 float

Question

Is there some clever and reliable way to print series of bits as an IEEE-754 without actually using a float type?

I have found a way to print fractions, which allows me to represent the float as aa fraction. However, I then came to realize that the exponent may range from -127 to 128 (after adjusting with bias), which may result in the multiplication mantissa * 2^128 . The fraction method relies on representing the numerator as an integer, and I would require a really large integer to do this multiplication. I mean, I could use "custom" type to represent this large value (ie https://gmplib.org/ ), but I would prefer if to avoid this. If we multiplied by 10^x, I could simply adjust the decimal point and add some zeros, but sadly that's not the case either.

I have not been able to find anything that mentions any solution for this. Probably due to the fact that googling stuff like "print from

Why am I actually trying to do this?
I'm only doing this to get a better understanding of how floats (IEEE-754 in particular) work, and I find that it always help to do some practical example. So I thought "Hey, why not try to code it?". This has no practical application (that I know of)!

Answer 1

So, almost immediately after posting this, I finally succeded in finding the resources I've been looking for.

https://www.ryanjuckett.com/printing-floating-point-numbers/ talks about it, and references other relevant sources.