For the following circuit design questions, you must show the procedure of obtaining the truth-table, obtaining the simplified logic function using k-map, and drawing logic diagram.

8. (a) Design a half-subtractor circuit with inputs x and y and outputs Diff and Bout . The circuit subtracts the bits x y and places the difference in D and the borrow in Bout.

(b) Design a full-subtractor circuit with three inputs x, y, Bin and two outputs Diff and Bout. The circuit subtracts x y Bin, where B in is the input borrow, Bout is the output borrow, and Diff is the difference.