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Offline blinky87Topic starter

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boolean logic question
« on: November 13, 2019, 09:32:21 pm »
Hi everyone

Practicing some Boolean logic which I want to simplify and make a circuit from eventually.

The scenario I found states that Q can be equal to 1 providing one of both statements are true.
~A AND B
or
A AND B AND ~C

I can construct the truth table for the second argument, but since the first argument does not contain C, how is this represented in the truth table? Like this?

https://imgur.com/a/avYZwJ8
 

Offline Wimberleytech

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Re: boolean logic question
« Reply #1 on: November 13, 2019, 09:40:56 pm »
Hi everyone

Practicing some Boolean logic which I want to simplify and make a circuit from eventually.

The scenario I found states that Q can be equal to 1 providing one of both statements are true.
~A AND B
or
A AND B AND ~C

I can construct the truth table for the second argument, but since the first argument does not contain C, how is this represented in the truth table? Like this?

https://imgur.com/a/avYZwJ8

The first argument generates a results that is ORed with a result of the second argument.  Both arguments do not need to contain C.  The layout of your truth table is fine but it is missing a state and also has an error.
« Last Edit: November 13, 2019, 09:42:39 pm by Wimberleytech »
 

Offline blinky87Topic starter

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Re: boolean logic question
« Reply #2 on: November 13, 2019, 09:59:03 pm »
Thank you for your help!

I have amended the truth table;

https://imgur.com/a/W3cU43e
 

Offline Wimberleytech

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Re: boolean logic question
« Reply #3 on: November 13, 2019, 10:01:42 pm »
Thank you for your help!

I have amended the truth table;

https://imgur.com/a/W3cU43e

You added the missing state.  Now do the boolean analysis of the last state using the two expressions ORed with each other.
 

Offline rstofer

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Re: boolean logic question
« Reply #4 on: November 13, 2019, 10:56:07 pm »
The Truth Table is the least usable way of describing the problem.  You really should use Karnaugh Maps because the simplification is immediately apparent.  This is going to be CRUDE


A/B   C'  C
------------
0 0 | 0   0
0 1 | 1   1
1 1 | 1   0
1 0 | 0   0


Draw an ellipse around the two 1's in the left column under C' and you get B & C'  -- A is eliminated because it changes between the two rows
Draw an ellipse around the two 1's in the second row and you get A' & B  -- C is eliminated because it changes between the two columns
Combine terms B & (A' + C')
The Karnaugh Map is a lot like a Truth Table except that only one variable can change between adjacent rows or adjacent columns.  That's why the minimization shows up naturally.
http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/karnaugh.html
« Last Edit: November 13, 2019, 11:05:34 pm by rstofer »
 

Offline blinky87Topic starter

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Re: boolean logic question
« Reply #5 on: November 13, 2019, 11:07:43 pm »
My outcome is to use K-maps, I just didn;t want to overly complicate things just yet. One step at a time :D. But yes, thank you!!!!
...and thank you both for helping.

The k-map result I got is A'B + BC'
which is the same as yours I believe, however, you have factored out.

I was just going through creating the truth table again and noticed I have Q = 1 when B & C. I'm struggling to work this out but I don't think I'm carrying the result through the combination circuit i.e. I am only taking into account the one output, Q.
« Last Edit: November 14, 2019, 12:01:46 am by blinky87 »
 

Offline onlooker

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Re: boolean logic question
« Reply #6 on: November 13, 2019, 11:27:48 pm »
Q =  A'*B + A*B*C'   =   B*(A' + A*C')   =   B*[A'*(1+C') + A*C']

   =  B*(A'*1 + A'*C' + A*C')  =  B*[A' + (A'+A)*C']

   =  B*(A'+C')  =  B*(A*C)'
 

Offline Wimberleytech

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Re: boolean logic question
« Reply #7 on: November 14, 2019, 03:21:08 am »
Thank you for your help!

I have amended the truth table;

https://imgur.com/a/W3cU43e

You added the missing state.  Now do the boolean analysis of the last state using the two expressions ORed with each other.

Looking back I realized that I had ~A inverted in my notes.
 


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