You could do this by checking each pixel and comparing it to the adjacent pixels. This will help you decide if the black pixel is in the black square or not, same for white pixels.
What you want to do is essentially apply the pattern picture on the right at the target picture on the left, so that will act as an arithmetic or logic filter. For the example above, you should use some Pattern Matching algorithm just for obtain the exact place at where you will superimpose one over other.