Is this truth table hitting all the possible cases?

In summary, the conversation is about checking the truth table for a circuit before implementing it. The problem involves six sensors and a master switch, with outputs for an alarm, lights, video cameras, and a call to the police. The concern is that there may be too few possibilities or rows for the sensors. Ultimately, it is determined that the truth table is correct.
  • #1
mr_coffee
1,629
1
Hello everyone, I don't want to implement the rest of this circuit if i messed the truth table up! So i was wondering if someone can take a look to see if the truth table seems to hit all the cases and looks correct.
http://img417.imageshack.us/img417/6629/lastscan4hi.jpg
Here is what the problem says:
Inputs:
<tex>S_i = 0, 1, 2, 3, 4, 5</tex> - signals from six sensors sets (0 - instrution detected, 1 - no intrusion detected).
M- master switch (0- security system on, 1- security system off)

Outputs:
A- alarm (0 - alarm on, 1- alarm off)
L - lights (0 - lights on, 1 - lights off)
V - video cameras (0 - video cameras OFF, 1 - video cameras ON)
C- call to police (0 - call OFF, 1- call ON);

Thanks!
 
Last edited by a moderator:
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  • #2
n/m, it is right.
 
  • #3
Since you have inputs 0-5 and we only care about when M is on except for the one case when it is off, shouldn't there be 2^(n-1) possibilities or rows for the sensors?
 

What is a truth table?

A truth table is a way of visually representing the possible combinations of inputs and outputs for a logical expression or statement. It shows all the possible cases and the resulting truth values for each case.

How do I know if a truth table is hitting all possible cases?

A truth table is considered complete or hitting all possible cases when it includes every possible combination of inputs and their corresponding outputs. This means that there are no missing or duplicate rows in the table.

Why is it important for a truth table to hit all possible cases?

A complete truth table ensures that all possible scenarios have been considered and accounted for in a logical expression. This helps to verify the validity and accuracy of the statement and can also be used to identify any inconsistencies or errors.

What happens if a truth table does not hit all possible cases?

If a truth table is incomplete, it means that there are some input combinations that have not been accounted for. This can lead to errors in logical statements and can make it difficult to accurately evaluate the truth value of the statement.

Are there any shortcuts for creating a truth table?

There are some techniques and shortcuts that can be used to create a truth table more efficiently, such as using logical equivalences and simplifying the statement before constructing the table. However, it is important to always double-check and make sure that the truth table includes all possible cases.

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