522 to base two

(i'm struggling so bad with math :,))

 1000001010 base 2

Explanation:

There are two methods to solving this problem.

One method is to involve having a list of the powers of 2

And so on.

In that list should be 2^9 = 512. So 512 is a power of 2. It is the largest such power that is just under 522. Subtracting it off gets us

522-512 = 10

So that explains why the 2^9 slot in the answer is a '1'. This is the first '1' mentioned in the answer shown above. Then we have a string of '0's until we reach 1010 at the end. That long string of 0s indicate that we don't have any of the following powers: 2^8, 2^7, 2^6, 2^5, 2^4

It's when we get to 2^3 is when we finally have a power of 2 to add on.

Then note how 10-2^3 = 10-8 = 2

So the last term we need to add on is 2^1 = 2. Note the gap from 2^3 to 2^1 because of the first 0 in 1010

So that's how we end up with 1000001010 as our final answer.

the graph on the bottom right