A simple security system for two doors consists of a card reader and a keypad.

A person may open a particular door if he or she has a card containing the corresponding code and enters an authorized keypad code for that card. The outputs from the card reader are as follows:
ConditionA   B
No card inserted 0 0
Valid code for door1 0 1
Valid code for door2 1 0
Invalid card code 1 1






To unlock a door, a person must hold down the proper keys on the keypad and, then, insert the card in the reader. The authorized keypad codes for door1 are 001, 011, 101 and111 and authorized keypad codes for door2 are 000, 010, 100 and 110. If the card has an invalid code or if the wrong keypad code is entered, the alarm will ring when the card is inserted. If the correct keypad code is entered, the corresponding door will be unlocked when the card is inserted.
Design the logic circuit for this simple security system. Your circuit’s inputs will consist of a card code AB, and a keypad code CDE. The circuit will have three outputs XYZ (if X or Y=1, door1 or 2 will be opened; if Z=1, the alarm will sound). Implement your circuit under the following hardware limitations:
a. Use 8:1 line multiplexer to realize X. Take CDE as selection inputs.
b. Use 5:32 lines decoder constructed from two 4:16 line decoders; decoding logic and an external OR gate to realize Y.
c. Use minimum number of NAND gates to realize Z.