Question
Boolean Algebra
A Simple Security System 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: 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 Oil. 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 (X=l 4 door 1 will be opened, Y=1 rightarrow door 2 will be opened, Z=1 rightarrow the alarm will sound). Design your circuit using only 2, 3, and 4-input NOR gates ( and inverters at the input). Use switches for inputs A, B, C, D, and E when you test your circuit.1 Design the circuit security system described 2.Have a test data set ready to demonstrate circuit operation. Note: data set should not be exhaustive; but large enough to test all cases. 3.Be ready to show your design work and to give a demo.
Explanation / Answer
From the information provided
X = a' bc ( d'e + ed' )
Y = abe (cd' + dc' )
Z = ab' + a'b'c' + a'b'c + a'bc' +ab'c' + abc
Now we have to use only of NOR gates
so we have to use de-morgan theorem and then we can easily get whole expression in terns of sum and bar so we get only NOR gates
