it kind of seems clumsy though. how would you know how to represent 571 as a combination of different powers of 2's quickly and easily. do you start with the highest power of 2 you can get without exceeding the number, and then just stumble your way through the lower powers?
EDIT: wait, i think i got it, lemme check
EDIT 2: yeah, i got it, it wasn't as tedious as i thought it would be. that's nice!
We have a 1 in each place where that is a power of two.
See that there is but none of but there is a .
Thus we see 10001… . That is, there is a 1 where there is a power of two.
From right to left, there are ones in the first two positions but a zero in the third position because there is no .
that method (as well as your method) is shown here
look at the "Short division by 2 with remainder" section for the method i described