Question

An Intrusion Alarm (F) will sound (set or on) if either one of two doors (X and Y) is open (on), and the Alarm Bypass (Q) is not set (off). The Alarm Bypass (Q) is used to test the system. If the Alarm Bypass (Q) is set (on) and the door (Z) is off, then the Intrusion Alarm (F) will sound (on), regardless of the condition of doors X and Y.

I am tasked with "Write a Boolean equation that describes when the Intrusion Alarm (F) is set using doors X, Y, and Z as well as the Alarm Bypass (Q)."

Can you please explain how this is done for my understanding? I see there are some posts on here that just simply state the equation is however i am not sure if that is correct, and how that was determined.

If you could also help explain how once i have the boolean expression, how i can convert that to logic to be used for a truth table that would be great as well.

Answer 1

Boolean equation for the Intrusion Alarm (F) is F = (X + Y) • (~Q) + Q • (~Z). To create a truth table, list all possible states for X, Y, Z, and Q, and determine F's state using the boolean expression.

Step-by-step explanation:

To write a Boolean equation that describes when the Intrusion Alarm (F) is set using doors X, Y, and Z as well as the Alarm Bypass (Q), we need to consider two scenarios as described in the question:

• If either door X or door Y is open and the Alarm Bypass (Q) is not set, the Intrusion Alarm (F) will sound. This can be represented as (X + Y) • (~Q) where '+' represents OR, '•' represents AND, and '~' represents NOT.
• If the Alarm Bypass (Q) is set and door Z is closed, the Intrusion Alarm (F) will also sound. This is represented as Q • (~Z).

The overall boolean expression combining both scenarios, using OR, since the alarm can sound in either condition, is:

F = (X + Y) • (~Q) + Q • (~Z)

To use this expression to create a truth table, you would list all possible combinations of input states for X, Y, Z, and Q (16 combinations total since each can be on or off), and then apply the boolean expression to each set to determine if F is on or off as a result.