(a) Design a combinational circuit with three inputs, A, B and C, and three outputs, X, Y, and Z. When the decimal equivalent of the binary input is 0, 2, 4, or 6, the corresponding binary output is one value more than the input (increase by one). When the decimial equivalent of the binary input is 1, 3, 5, and 7, the corresponding binary output is one value less than the input (decrease by one). Perform the following steps: i) Derive the truth table. (2 marks) ii) From the Lulli table, obtain tuc Boulcan Expressions for X, Y, and Zin luc Sum of Products (SOP) form (1.5 marks) il) Simplify the Boolean expressions for X, Y, and Z by applying Boolean algebra rules and laws. (1.5 marks)