It’s fun to posit these ideas by going in the intuitive direction, then going in the reverse direction and seeing what happens. I recently found this to be hel

It’s fun to posit these ideas by going in the intuitive direction, then going in the reverse direction and seeing what happens. I recently found this to be helpful when investigation fixed and floating point numbers. If ”1011” means 2^3 + 2^1 + 2^0, which is 11 the “1011.101” means the same thing but with an additional 2^-1 + 2^-3 aka 5/8. Negative powers seem weird to begin with but it kind of just is there to just discover, due to the symmetry. This kind of arithmetic is far less fundamental than what you and the article are talking about — it is just representation really, in computers — but I think it is a good example of how if you can tread a path in one direction then turning around and coming back to where you started then carrying on in the other direction is a useful tool for teaching and learning.