THEgdfg Objective: Design and implement a special purpose system that allows access to doors $1$ and $2($D$1$ and

D$2$ respectively$)$ by persons who have been given a valid four$-$bit binary code. The code is entered using

four switches: S$1,$ S$2,$ S$3,$ and S$4.$ Each valid switch can be set to $0$ or $1.$ The system gives access to doors

according to the following scheme:

a$)$ D$1$ if $0101$ or $1110$ is entered.

b$)$ D$1$ and D$2$ if $0111$ is entered.

c$)$ D$2$ 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.

Construct your circuit in Logisim. PLEASE DRAW RESULTING CIRCUIT SO I HAVE A BETTER UNDERSTANDING OF HOW THE FINAL RESULT SHOULD LOOK..... THANK YOU!!!