Base conversion - the LOGIC and INTUITION behind it

[O.J.]

Base conversion -- the LOGIC and INTUITION behind it...

for example, converting from base 10 to 2, a systematic way is to divide the number by 2's successively and keep track of the remainder. the remainder coefficients represent the binary number. Now why does this work is beyond me but I would love to know the idea behind it?

second, I am a bit unsure that you can represent each number using any base. e.g. write 7 to base 8?

 

[NoTime]

Try looking at this.

https://www.physicsforums.com/showthread.php?t=182526

 

[O.J.]

forget my 2nd question. Explain to me the logic on the systematic way of converting from decimal to binary (& other bases in general), please.