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boolean logic question
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blinky87:
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
Wimberleytech:

--- Quote from: blinky87 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

--- End quote ---

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.
blinky87:
Thank you for your help!

I have amended the truth table;

https://imgur.com/a/W3cU43e
Wimberleytech:

--- Quote from: blinky87 on November 13, 2019, 09:59:03 pm ---Thank you for your help!

I have amended the truth table;

https://imgur.com/a/W3cU43e

--- End quote ---

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