Question

You have been hired by a home security company to design and implement a home alarm

system. The logic of the system is as follows: once the alarm system has been armed, it is to

sound if the front door is opened, the back door is opened or either of two windows is

opened (you can assume there are only two windows).

Design the necessary circuit to implement the situation described above.

Your circuit should have five inputs (A = alarm, F = front door, B = back door, W1 = window

1 and W2 = window 2). A = 1 means the system is armed; A = 0 means it is disarmed. F = 1

means the front door is open; F = 0 means it is closed. (Similarly for the back door and the

windows.) There should be one output, S. When S = 1 the alarm should sound; S = 0

means the alarm is silent. Please use these letters to indicate the inputs and the output

Be CAREFUL to get the correct function for your five inputs before simplifying and designing the circuit. You should minimize the circuit. Your inputs and output should be labeled.

please include the following:

• Drawing of your completed circuit including all appropriate labels.
• Truth tables for the circuit (use Word table feature)
• Kmap for the circuit (use Word table feature)
• Details (show your work) on what was done to simplify the circuit
• A brief written summary (250 to 500 words) of the process you followed, decisions made in laying out the circuit, etc..
• IMPORTANT: please include an explanation on how you put together the kmap based on the truth table, how you made the groupings on the kmap, and how you were able to simplify them in order to create the final circuit

Answer 1

Solution :

In the given question, the truth table will have 5 entries each for the doors, front and back and two windows and the alarm being armed. Based on the question, if any of the front door, back door or either of the two windows are open and having the alarm armed will lead to the sounding of alarm.

So we will have 5 input in the truth table and one output representing S called as alarm sound. If any of the the doors or windows have corresponding 1's in a particular row will lead to the sounding of alarm and hence S set its state to 1.

From the top of the truth table to the half way mark, all the the the the output are zero since the alarm is not armed (A=0). And for the alarm being armed, the required output will be based on the conditions mentioned above.

We have 32 rows in our truth table so it is required to create a k map for five inputs. To avoid the large ke map we will take a shortcut of setting A to 1 and creating the k map for the second half of the truth table from row 16 to 31. For this portion A is fixed at 1 only. Therefore in the final equation A will be ANDed to the final expression. Now We combine and form loop in the k map to reach a conclusive final reduced expression. And at last, we make circuitry according to the final expression and mentioned the number of different types of logic gates used in the the finalized circuit.

I have tried to explain it in very simple language and
I hope that i have answered your question satisfactorily.Leave doubts in comment section if any.