# Division method for base-conversion

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.

When you write a number in base $$2$$ the non zero numbers are remainders in dividing by powers of two. For example $$15$$ is written as $$1111$$ that means if you divide it by two the remainder is one . $$15=2\times 7+1$$ Now if you divide $$7$$ by two the remainder is $$1$$ and so forth.