IV Design Question using the usual Logic gates. $(20$ points$)$

$(10$points$)$Consider the addition of two one$-$digit binary numbers a and b$.$

The four possible valuations of $a,b$ and the resulting sums are

$\backslash$table$[[a,0,0,1,1],[+b,,,,],[s_1{s}_0,,,,]],\frac{+0}{00},\frac{+1}{01},\frac{+0}{01},\frac{+1}{10}$

Design the logical circuit to implement the adder.