Anti-aliasing (images) - how does it work?

I understand correctly that image smoothing works as follows:

I have a 2x2 image block consisting of individual pixels (x):

x  |  x
¬¬¬¬¬¬¬
x  |  x

I want to smooth the image using the following values:

3  |  4
¬¬¬¬¬¬¬
2  |  1

Therefore, whether the 2x2 block will be displayed as:

x x | x x
x   | x x
¬¬¬¬¬¬¬¬¬
x x | x 
    | 

It is right? If so, did I correctly illustrate the correct pixel layouts?

Or am I completely mistaken? If so, can someone kindly enlighten me (ideally with an example)?

I know that the sample size that I chose to use is small, but it was just for illustration.

Many thanks.