Question

I’m trying to understand the reason for a rule when converting.
I’m sure there must be a simple explanation, but I can’t seem to wrap my head around it.
Appreciate any help!

Converting from base10 to any other base is done like this:

number / desiredBase = number + remainder

You do this until number = 0.

But after all of the calculations, you have to take all the remainders upside down. I don’t understand why.

For example: base10 number to base2

11 / 2 = 5 + 1
5 / 2  = 2 + 1
2 / 2  = 1 + 0
1 / 2  = 0 + 1

Why is the correct answer: 1011 and not 1101 ?

I know it’s a little petty, but it would really help me remember better if I could understand this.

Answer 1

Think of the same in decimal system, even if it doesn’t make that much sense to actually do the math in this case 🙂

1234 / 10 = 123 | 4
123 / 10  = 12  | 3
12 / 10   = 1   | 2
1 / 10    = 0   | 1

Every time you divide, you strip the least significant digit, so the first result, is the least significant result — digit on the right.