There is an article called “The Base-Conversion method:Why does it work?” (The Base-Conversion method:Why does it work?),which states that:
Each time you divide, you're asking "Does the original number contain a multiple of this power of two?", and the remainder is either telling you "yes" (with a "0") or "no" (with a "1")”.
I have checked it on many examples and it really works,but I can not understand why. Could you please explain.
Thanks in advance.