Thread: Truth Table --> Logical Expressions
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Old Jun 2nd, 2006, 6:02 PM   #1
Sane
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Exclamation Truth Table --> Logical Expressions
I'd like to convert the following truth table in to a logical expression:

(Toggle Plain Text) 
INPUT                   OUTPUT
[0, 0, 0, 0, 0, 0, 0] [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0]
[0, 0, 0, 0, 0, 0, 1] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 1, 0] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]
[0, 0, 0, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1]
[0, 0, 0, 0, 1, 0, 0] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]
[0, 0, 0, 0, 1, 0, 1] [1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1]
[0, 0, 0, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1]
[0, 0, 0, 0, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 1, 0, 0, 0] [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1]
[0, 0, 0, 1, 0, 0, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1]
[0, 0, 0, 1, 0, 1, 0] [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]
[0, 0, 0, 1, 0, 1, 1] [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 1, 1, 0, 0] [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1]
[0, 0, 0, 1, 1, 0, 1] [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1]
[0, 0, 0, 1, 1, 1, 0] [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]
[0, 0, 0, 1, 1, 1, 1] [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1]
[0, 0, 1, 0, 0, 0, 0] [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1]
[0, 0, 1, 0, 0, 0, 1] [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 1, 0] [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]
[0, 0, 1, 0, 0, 1, 1] [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1]
[0, 0, 1, 0, 1, 0, 0] [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0]
[0, 0, 1, 0, 1, 0, 1] [1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 1, 1, 0] [1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1]
[0, 0, 1, 0, 1, 1, 1] [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1]
[0, 0, 1, 1, 0, 0, 0] [1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1]
[0, 0, 1, 1, 0, 0, 1] [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]
[0, 0, 1, 1, 0, 1, 0] [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]
[0, 0, 1, 1, 0, 1, 1] [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 1, 1, 1, 0, 0] [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1]
[0, 0, 1, 1, 1, 0, 1] [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1]
[0, 0, 1, 1, 1, 1, 0] [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0]
[0, 0, 1, 1, 1, 1, 1] [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0, 0] [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1]
[0, 1, 0, 0, 0, 0, 1] [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1]
[0, 1, 0, 0, 0, 1, 0] [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1]
[0, 1, 0, 0, 0, 1, 1] [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1]
[0, 1, 0, 0, 1, 0, 0] [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1]
[0, 1, 0, 0, 1, 0, 1] [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 1, 0, 0, 1, 1, 0] [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]
[0, 1, 0, 0, 1, 1, 1] [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1]
[0, 1, 0, 1, 0, 0, 0] [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[0, 1, 0, 1, 0, 0, 1] [0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0]
[0, 1, 0, 1, 0, 1, 0] [0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1]
[0, 1, 0, 1, 0, 1, 1] [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1]
[0, 1, 0, 1, 1, 0, 0] [0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1]
[0, 1, 0, 1, 1, 0, 1] [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]
[0, 1, 0, 1, 1, 1, 0] [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]
[0, 1, 0, 1, 1, 1, 1] [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 1, 1, 0, 0, 0, 0] [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[0, 1, 1, 0, 0, 0, 1] [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]
[0, 1, 1, 0, 0, 1, 0] [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[0, 1, 1, 0, 0, 1, 1] [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0]
[0, 1, 1, 0, 1, 0, 0] [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1]
[0, 1, 1, 0, 1, 0, 1] [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1]
[0, 1, 1, 0, 1, 1, 0] [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1]
[0, 1, 1, 0, 1, 1, 1] [1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]
[0, 1, 1, 1, 0, 0, 0] [1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]
[0, 1, 1, 1, 0, 0, 1] [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 1, 1, 1, 0, 1, 0] [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[0, 1, 1, 1, 0, 1, 1] [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]
[0, 1, 1, 1, 1, 0, 0] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[0, 1, 1, 1, 1, 0, 1] [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]
[0, 1, 1, 1, 1, 1, 0] [1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1]
[0, 1, 1, 1, 1, 1, 1] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]
[1, 0, 0, 0, 0, 0, 0] [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1]
[1, 0, 0, 0, 0, 0, 1] [1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1]
[1, 0, 0, 0, 0, 1, 0] [1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]
[1, 0, 0, 0, 0, 1, 1] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[1, 0, 0, 0, 1, 0, 0] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[1, 0, 0, 0, 1, 0, 1] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1]
[1, 0, 0, 0, 1, 1, 0] [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]
[1, 0, 0, 0, 1, 1, 1] [1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]
[1, 0, 0, 1, 0, 0, 0] [1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1]
[1, 0, 0, 1, 0, 0, 1] [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1]
[1, 0, 0, 1, 0, 1, 0] [1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]
[1, 0, 0, 1, 0, 1, 1] [1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1]
[1, 0, 0, 1, 1, 0, 0] [1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1]
[1, 0, 0, 1, 1, 0, 1] [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]
[1, 0, 0, 1, 1, 1, 0] [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]
[1, 0, 0, 1, 1, 1, 1] [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1]
[1, 0, 1, 0, 0, 0, 0] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[1, 0, 1, 0, 0, 0, 1] [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0] [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1]
[1, 0, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]
[1, 0, 1, 0, 1, 0, 0] [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1]
[1, 0, 1, 0, 1, 0, 1] [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1]
[1, 0, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]
[1, 0, 1, 0, 1, 1, 1] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[1, 0, 1, 1, 0, 0, 0] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[1, 0, 1, 1, 0, 0, 1] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1]
[1, 0, 1, 1, 0, 1, 0] [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[1, 0, 1, 1, 0, 1, 1] [1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0]
[1, 0, 1, 1, 1, 0, 0] [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1]
[1, 0, 1, 1, 1, 0, 1] [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1]
[1, 0, 1, 1, 1, 1, 0] [1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1]
[1, 0, 1, 1, 1, 1, 1] [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]
[1, 1, 0, 0, 0, 0, 0] [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]
[1, 1, 0, 0, 0, 0, 1] [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[1, 1, 0, 0, 0, 1, 0] [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[1, 1, 0, 0, 0, 1, 1] [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]

The program would output fourteen logical expressions (one for each column in the output). Is there a program that can do this for me? If not, how would you assume is the best way to do it? It doesn't have to be perfectly optimized logic, but that would surely help.


An example of what the program could do:

(Toggle Plain Text) 
INPUT  OUTPUT
[0, 0]  [1]
[0, 1]  [0]
[1, 0]  [0]
[1, 1]  [0]

Then the program would output: A2 = A1 nor B1


A way to look at it is one expression for each column in the output. So all that has to be made sure is that the seven inputs in my first example, can achieve all the results in _X_ column of the output with a certain logical expression. Then this is repeated for all the columns in the output table.
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