What is the Big O of bit count? I'm not sure how the method works, but I would assume it is done in O(logn).
Specifically with this code (where x = 4, y = 1):
return Integer.bitCount(x^y);
Given its implementation, the method consists of six O(1) statements performed in sequence, so it's O(1).
public static int bitCount(int i) {
// HD, Figure 5-2
i = i - ((i >>> 1) & 0x55555555);
i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
i = (i + (i >>> 4)) & 0x0f0f0f0f;
i = i + (i >>> 8);
i = i + (i >>> 16);
return i & 0x3f;
}