[dntbnmpls]

The formula makes sense, but it doesn't give you the full picture of floating points. The formula doesn't explain NaN, positive infinity, negative infinity or even the bias. I think seeing the layout of a floating point number and their constituent parts in memory is more instructive than a formula.

Floating points, like two's complement, are hardware derived/limited creations. You have to understand the underlying hardware and binary limitations to understand why they exist and why they were created in that manner. The same thing applies to ascii. Zero is 48, A is 65 and a is 97. The mapping seems arbitrary unless you see the bit pattern and you realize how clever the design is and the reason why some of the symbols got their mappings in ascii.