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I have a karnaugh map question. In the Digital Design course teacher learnt but I couldn't understand here clear. We can see in the picture. In the first one, we use all 1s and have 4x3 1s. In the second one we have 8x2 1s and we use some 1s two times. Which answer is true? 1st one or 2nd one? Why?

enter image description here

Thanks for all responses.

MattClarke
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user119949
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1 Answers1

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Both are valid expressions for the illustrated function.

In most contexts A+C would be preferred since it is a simpler expression.

MattClarke
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  • OK. Both are valid but they have to be equal(Am I Wrong?).Then A'C + AC' + AC = A + C | A'C + A(C'+C) = A + C | A'C + A = A + C | A'C = C | A' = 1 | A = 0 I found that A have to be 0 to provide equality. I proved above if A = 1 Then 1st one is not equal to 2nd one. However if we look truth table, their truth tables are same. Finally, I am confused. – user119949 Oct 28 '14 at 18:31
  • In this context "valid" means "an expression whose truth values match those in the KM". And "equal" means "the expressions both have exactly the same truth assignments" -- i.e. whenever one expression has a boolean value of 1, so does the other. So how would you show that `A'C+AC'+AC` and `A+C` are equal? One way would be to construct a KM for each separately and see if they are the same. But wait! That's already been done! If an expression X is a valid expression of a KM and Y is another valid expression of the same KM then of course X and Y must be equal. – MattClarke Oct 28 '14 at 22:22