b) Design a combinational circuit with three inputs, x, y, and z, and three outputs, A, B, and C. When the binary input is 0, 1, 2, or 5, the binary output is two greater than the input. When the binary input is 3, 4, 6, of 7, the binary output is three less than the input (1) Construct the truth table for the given problem (ii) Find the standard SOP for the given problem. Implement the Boolean Functions using a decoder constructed with NAND gates and NAND OT AND gates connected to the outputs. Minimize the number of inputs in the extemal gates (iv) Show how the same Boolean functions can be implemented using a demultiplexer. (111