Chess puzzle

hi all,

I recently started a new town and it has the chess puzzle in it. The first puzzle I 'accidentally' solved without fully understanding the mechanics. Now I am at the next level and I just don't understand how it should work.

I can see the four clues surrounding the pawns and I feel like I already solved the puzzle but apparently I didn't. How should I use the clues? 

Let's say I have 

https://imgur.com/1oPvaBg

Where the last row is the row I can change.

Now I have four clues, say one is P W W (top to bottom). What do I do with this? Does it mean the first column is correct as it already contains P W W?

The four clues are as follows btw:

https://imgur.com/9LT6Ydv

https://imgur.com/undefined

https://imgur.com/o8pIBbl

https://imgur.com/wZXXxFy

!!SPOILER!!

You start on the other end, with the right column. 

Say the black ones are 0 and the white ones are 1.

So the right (1st) column is correct as 1 + 0 = 1

Then it gets a bit tricky in this particular puzzle as the 2nd column is 1 + 1, but there is no 2. As per the 4th clue you posted, whenever you get 1 + 1, you put a 0 at the bottom of that column and add a 1 to the next column.

Then it gets even trickier for you, because with adding another 1 to your third column, you get 1 + 1 + 1! In those cases you put a 1 at the bottom of that column and add a 1 to the next one.

That makes your 4th column 1 + 0 + 0 = 1

And your 5th column is already correct as 0 + 1 = 1.

So, starting at the right column, your solution is 1 0 1 1 1