# Creating a logic function of a burglar alarm system for a bank

This is the problem from homework that I am stuck on:

A burglar alarm system for a bank is to be operative only if a master switch at the police station has been turned on. Subject to this condition, the alarm will ring if the vault door is disturbed in any way, or if the door to the bank is opened unless a special switch is first operated by the security guard's key. The vault door will be equipped with a vibration sensor that will cause a switch to close if the vault door is disturbed, and a switch will be mounted on the bank door in such a way that it will close whenever the bank door is opened. Symbolize the above system as a logic function and construct the corresponding logic diagram.

So, I created an outline to list the conditions and the actions:

Conditions:

• A = Master switch is turned on
• B = Vault door is disturbed in any way
• C = Vault door is opened
• D = Special switch is 1st operated by security guard's key

Actions:

• W = Burglar alarm system becomes operative
• X = Alarm rings
• Y = Switch closes
• Z = Switch mounts on bank door in such a way it will close the door

And here's the truth table:

\begin{array}{c c c c|c c c c} A & B & C & D & W & X & Y & Z \\ \hline 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0\\ 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0\\ 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\ 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0\\ 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1\\ 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0\\ 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0\\ 1 & 1 & 0 & 1 & 1\\ 1 & 1 & 1 & 0 & 1 & 1\\ 1 & 1 & 1 & 1 & 1\\ \end{array}

It is the last three I am not sure about:

• What happens if the door is disturbed AND the special switch is first operated at same time? Would the alarm still ring?
• Would the vibration sensor still be activated when the door is opened (i.e., what would happen if the door is open and is disturbed at same time)?

I am not very knowledgeable with how bank security system works, so it would be nice if anyone can explain about it.

• Knowledge of bank systems isn't important. – Andy aka Sep 14 '14 at 16:31
• Yay, a decent homework question that shows what you've worked on so far! – JYelton Sep 14 '14 at 18:03
• Switch mounts on bank door in such a way it will close the door is wrong. It really is switch mounts on bank door in such a way that it will close (activate) when the door is open – slebetman Sep 14 '14 at 19:42

Oh, take a step back a little from it first and look at the different parts of it.

What stimulus, ignoring the extra conditions, would make the alarm sound? Simple:

1. someone tampers with the vault -OR-
2. someone opens the bank door.

Now, when would those stimuli cause the alarm to sound? Again, simple - when the alarm is armed. When is it considered armed?

1. when it has been switched on at the police station -AND NOT-
2. when the guard's switch has been activated.

So, if it is armed -AND- triggered, then sound the alarm.

So you have three truth tables. Firstly the trigger:

A = vault, B = door, Q = alarm.

\begin{array}{c c|c} A&B&Q\\ \hline 0&0&0\\ 0&1&1\\ 1&0&1\\ 1&1&1\\ \end{array} Then you have the armed table:

A = police station, B = guard's switch \begin{array}{c c|c} A&B&Q\\ \hline 0&0&0\\ 0&1&0\\ 1&0&1\\ 1&1&0\\ \end{array} And then you combine them together into the alarm sounding table:

A = triggered, B = armed \begin{array}{c c|c} A&B&Q\\ \hline 0&0&0\\ 0&1&0\\ 1&0&0\\ 1&1&1\\ \end{array}

You could then combine them into one huge logic table if you wanted.

In boolean it could be expressed as:

$(Vault + Door) · Station · ¬Guard$