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: A, B, C, and D. Each valid switch can be set to 0 or 1. The system gives access to doors according to the following scheme:

D1 if 0101 or 1110 is entered.

D1 and D2 if 0111 is entered.

D2 if 0100 is entered.

Implement this using ONLY NAND gates meaning "not" inputs