Space complexity of the "add two binary strings" challenge
I agree with you, space complexity should be \$O(n)\$, using StringBuilder should not matter because, internally it would store char in an array which would expand / shrink as needed.

Now some code-reviews.

Error check:


Null check? x or y could be null. This (x == null || y == null) looks better.
Your code says "sumofbinary", but what if your string was "123" + "543"?


Name check:


sb is not a professional name, call it sum.


Syntax check:


while(i &gt; = 0 || j &gt;= 0) .. there is a space &gt; = for i &gt; = 0, but not for j. 


Misc:


StringBuilder can be marked final.
You end for loop when both i &amp; j are 0. This has a drawback, if i is longer than j, you would waste error checking if (j > 0).