Floats are genius

And so let's construct them from first principles.

The Goals

We want to represent a whole variety of numbers, with the largest possible range we can attain. We want to be able to do arithmetic on these numbers, and we want to be able to do it quickly. These are some tricky goals to achieve, but let's believe in ourself!

Restrictions from our goals

We want to do arithmetic quickly, so that will restrict us to binary. On the other hand, we have a limited number of