An "order of magnitude" has no precise numerical meaning, it depends on what base you're working in. If the log of the number in base b increases by 1, you've increased 1 order of magnitude with respect to that base. (I don't know why the parent said "20", my instinct is to say 14 orders of magnitude here.)
I've usually heard it being used to describe powers of 10. I'd be willing to accept 14 orders of magnitude since we're talking about powers of 2, but I still can't figure out where they got 20 from. Hence my question.