2x1 mux using half adder

how to design a 2x1 mux using half adder??

 

I googled but i couldnt find answer. I found many answers about how to build half adder using 2x1 mux

 

Truth table of mux: a is selected when s = 0 and b is selected when s =1
so the eqn is (b.s)+(a.sbar)
a b s o/p
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 1

For half adder the equation is sum = a^b and carry = a.b
truth table is as follows
a b sum cout
o o o o
o 1 1 o
1 o 1 o
1 1 o 1

HA circuit uses xor for sum, and gate for carry.now i want to implement the mux equation and if i give "a" and "s" as my input to xor gate, the output is = (a.sbar)+(abar.s). I dont want the term abar.s and that changes the result in some cases. So i am not knowing how to model the circuit using half adders.

Please give me some direction to go on.

 

I guess i figured out the solution.

i got it from careful observation of mux table. for a and b = 0/1 the output of mux is a.b i.e carry output of half adder.
for other values of a and b the output is (a xnor b). So i think if we take half adder
the input to xor gate are b and s and then invert the output of xor gate using another xor or just an inverter. to get the final output of mux we have to or the inverted sum and carry.

Please let me know if there is a better way