k map minimization digital logic

Question

What is the minimal $Sum-Of-Products$ of the map? ($X$ is a don't care)

Answer 1

Answer : $XY + ZY'$

To Cover, All the Four 1's, We can make Two  Subcubes of Size 4.

One Subcube will be made of all the cells of ROW-2 and will cover the minterms $5$ and $9$

Other Subcube will be made of the Cells corresponding to minterms $6,7,14,15$ and will cover the minterms $6,15$

Answer 2

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Comments

@ abhishekmehta4u

WHY not only take a sub cube of size 4 formed by cells (number- 5,7,13,15) which will yield  expression or o/p as "xz"?

Why did you selected sub cube with "xy"?

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• if EPI covers all the minterms then it is minimal sop . other wise select the additional prime implicants so that function covered complitlly and it should be minimal.
• here subcube 1 and 3 are EPI and it covers all one's . then why are you select subcube 2 . if we select then we need to three subcube which is not minimal and it is redundent.

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thank you very much.

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There are no Essential Prime Implicants here. because each 1 can be covered by at least two subcubes with the help of don’t cares.

PI=5

EPI=0