Apertures work in steps of
sqrt(2) -- i.e., each time you increase the area of the aperture, you double the amount of light that can go through the lens in a given period of time.
For simplicity, let's start with, say, f/2 and f/5.6. The full stops in this case are f/2, f/2.8, f/4 and f/5.6. That means changing f/2 to f/5.6 decreases the exposure by three stops. To compensate for that, you need a change of 3 stops in the ISO or shutter speed (or a combination of the two).
ISO numbers and shutter speeds both work exponentially -- i.e., multiplying or dividing by a fixed factor changes the amount of light translated by a fixed number of stops. To use your example, starting from ISO 100, going to ISO 200 is a one-stop increase, to ISO 400 is a two-stop increase, and ISO 800 is a three-stop increase.
That leaves us with one minor detail to deal with: fractional f/stops, which are kind of a pain. f/4.5 is about 1/3rd of a stop slower than f/4. If you started from f/1.4 and went to f/4.5, that would be ~3 1/3rd stops, so you'd need to increase the ISO by ~3 1/3rd stops to compensate. Starting from ISO 100, that works out to ISO 1000 (200, 400, 800, 1000[3 1/3]). Technically, ISO 1000 isn't quite right, but it's close enough for any practical purpose and it's what your camera will (probably) provide.