Objective: Design and implement a special purpose system that allows access to doors 1 and 2 (D1 and D2 respectively) by persons who have been given a valid four-bit binary code. The code is entered using four switches: S1, S2, S3, and S4. Each valid switch can be set to 0 or 1. The system gives access to doors according to the following scheme: a) D1 if 0101 or 1110 is entered. b) D1 and D2 if 0111 is entered. c) D2 if 0100 is entered. Derive your truth table and use this web site to simplify your circuit. Select 4-Variables and POS (Product of Sums) which will produce an OR-AND circuit. Implement your circuit only using NOR gates. The correct implementation of this circuit should only have two layers of NOR gates. The gates used to complement the inputs are not counted as the gate layers.