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f(x,y,z) = $\bar{x} +\bar{y}z + xz$

what are prime implicants of this switching function?
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2 Answers

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Prime Implicant $:$ A prime implicant is a product term obtained by combining the maximum possible number of  adjacent squares in the map.

Essential Prime Implicant $:$ Essential Prime Implicant is the subcube which covers at least one minterm which is not covered by any other prime implicants.

 

 

So the given switching function contains two PIs and that are EPIs too. 

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$f(x,y,z)=\sum_m(0,1,2,3,5,7)$ contains $2$ prime implicants $(0,1,2,3)$ and $(1,3,5,7)$ which is also EPI.

$\therefore f(x,y,z)=\sum_m(0,1,2,3,5,7)=\bar x+z $

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