converting any number system to binary an essential question.

Question

Why we write the remainder bottom to up from converting any number system to binary? We can write it from up to down, why not? And what is the logic here?

Answer 1

If you have a number written in binary and you want to know if it's even or odd, how do you tell? You look at the rightmost digit, don't you? Now when you convert some number to binary, the remainder of the first division tells you whether it's even or odd, right? So do you want to write it on the left or the right? On the right, of course. Put it where you would look for it!