A person may open a 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:

A B

No card inserted $00$

Valid code for door$101$

Valid code for door$211$

Invalid card code $10$

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 door$1$ are $3-$bit odd numbers whereas authorized keypad codes

for door$2$ are the $3-$bit even numbers. 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 inputs

will consist of a card code AB$,$ and a keypad code CDE. The circuit will

have three outputs XYZ $($if X or Y$=1,$ door$1$ or $2$ will be opened; if Z$=1,$ the

alarm will sound$).$ Implement the output function X with a $5$:$32$ decoder

constructed from four $3$:$8$ decoders using NAND gates with enable input

E$,$ one $2$:$4$ decoder $,$ and an external logic gate.