Below is given a description $($in some case with figure$)$ of the macroscopic state of a A$-$B alloy that mixes on square lattice. In each case you are asked for.

$(1)$ the total contigutational extropy is as function of $2N,$ the number of lattice sites

$(2)$ the entropy per lattice site in the thermodymaic limit $($i$.$e$.$ as $2N$ goes to infinity$).$

$($a$)$ A perfectly ordered system with compositon AB$,$ as shown below.

$($b$)$ Same systex as in $($a$)$ but with $1\%$ of the A atoms replaced by B atoms.