Writing a BASIC interpreter, with floating point, is much harder. Gates, Allen and other collaborators BASIC was pretty damned good.
[1] Bill & Steve (Jobs!) reminisce about floating point BASIC:
https://devblogs.microsoft.com/vbteam/bill-steve-jobs-remini...
What is hard is skipping the high level language step, and trying to do it in assembler in one step.
With fixed point numbers, you write the digits into the memory and have a convention that the decimal point is always after N-th digit. For example, if we agree that the point is always after 2-nd digit then a string 000123 is interpreted as 00.0123 and 123000 means 1230. Using this system with 6 digits we can represent numbers from 0 to 9999 to precision of 0.01.
With floating point, you write both decimal point position (which we call "exponent") and digits (called "mantissa"). Let's agree that the first two digits are the exponent (point position) and the rest four is mantissa. Then this number:
020123
That's all you need to know, and the rest should be easy to figure out.
1. the digits
2. the exponent
3. a sign bit
If you're familiar with scientific notation, yes, it's the same thing.
https://en.wikipedia.org/wiki/Scientific_notation
The rest is just the inevitable consequences of that.
And by the way engineering notation (where exponent must divide by 3) is so much better. I hate converting things like 2.234·10¹¹ into billions in my head.
And by the way (unrelated to floating point) mathematicians could make better names for things, for example instead of "numerator" and "denominator" they could use "upper" and "lower number". So much easier!