Build a 4-bit adder from four full adders. The inputs for this circuit will be the four bits for one 4-bit summand, $A_0, A_1, A_2, A_3$; another four bits for the other summand, $B_0, B_1, B_2, B_3$; and the carry-in for the right-most bit, $c_{\text {in }}$. Note that $c_{\text {in }}$ will be wired to 0 when using this as a stand alone 4-bit adder. What should the outputs be? What would the black box diagram for this 4-bit adder look like? Using your black box diagram, design an 8-bit adder.