(subtract)Inputs X; and Y, of each full adder in an arithmetic circuit have digital logic specified by the Boolean functions X_{\mathrm{i}}=A_{\mathrm{i}} \quad Y_{\mathrm{i}}=\bar{B}_{\mathrm{i}} S+B_{\mathrm{i}} \bar{C}_{\mathrm{in}} where S is a selection

variable, C is the input carry, and A, and B, are input data for stage i. (a) Draw the logic diagram for the 4-bit circuit, using full adders and multiplexers. (b) Determine the arithmetic operation performed for each of the four combinations of S and C: 00,01,10, and 11.