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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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