I have to minimise a boolean expression in SOP form having don't care conditions. I can do this by k-map but can I do this only using Boolean algebraic laws.
Q. Sigma(0,2,3,5,6,7,8,9) + d(10,11,12,13,14,15)
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What is a "don't care condition"? What do you mean by minimizing? What do the functions Sigma(..) and d(..) do? – Markus-Hermann Aug 31 '20 at 11:58
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The given lists of minterms and don't care terms can be transformed to one shorter list of implicants using Boolean laws.
The Karnaugh-Veitch map:
From the map or by inspection of the given 14 of 16 possible terms, it is clear that there are only two terms where the expression is false: 1 and 2.
Therefore, the expression can be written as
!(X0 & !X1 & !X2 & !X3) & !(!X0 & X1 & ! X2 & !X3)
Applying De Morgan's theorem:
(!X0 + X1 + X2 + X3) & (X0 + !X1 + X2 + X3)
Both factors share (X2 + X3) which can thus be factored out:
(!X0 + X1) & (X0 + X1) + X2 + X3
This leads to the result:
!X0 & !X1 + X0 & X1 + X2 + X3
We implicitely set all don't care terms to trueat the beginning. This was a good guess, but cannot be analytically derived without try-and-error.
Axel Kemper
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So there is no way to solve this algebraically without knowing the actual values of ' don't care conditions' ? – anas16 Aug 31 '20 at 20:05
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Try the [Karnaugh-Veitch](https://www.mathematik.uni-marburg.de/%7Ethormae/lectures/ti1/code/karnaughmap/) link in my answer. The online tool allows to experiment with different `d` values and their effect on the resulting expression. – Axel Kemper Aug 31 '20 at 20:41
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Yes I can do that by K-map but I have been given this question to do by boolean algebraic laws – anas16 Sep 01 '20 at 01:01