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Please answer letter B ONLY. Thank you.

Problem 2
A simple security system for two doors consist of a card reader and a keypad.
Card Reader -
* To Door 1
To Door 2
* To Alarm
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:
No card inserted
Valid code for door 1
Valid code for door 2
Invalid card code
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 101 and 110, and the authorized keypad
codes for door 2 are 101 and 011. 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 entered.
(a) Show the circuit's truth table.
Required format of the truth table in Problem 2(a). Inputs should be listed in ascending order. Show grid lines.
No other information table of any kind should be shown on your answer sheet except those indicated above.
(b) Determine the sum of all the input signals expressed in binary (discard insignificant zeros).
Show clearly the details of your solution.
(c) Derive the Boolean expression of each output signal X and Y using K-map.
NOTES: If the correct answer in Prob. 2(b) contains more 0's than I's use SOP otherwise use POS.
The basis of your choice should conform to the correct answer in Prob. 2(b).

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