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Consider the Karnaugh map given below, where X represents *"don't care" *and blank represents 0. what will be the SOP?

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Answer : Minimal SOP = $CA'$

To Cover all the 1's, We can make a Subcube of Size 4 which covers the cells corresponding to the minterms $1,3,9,11$ And Hence Covers all the 1's. So, Our required Minimal SOP = $CA'$

1. We can't make a Subcube of Size 8 here by covering all the cells marked by $1 \,\,and\,\,\times$ Because that'd be invalid.

2. We are only concerned for covering 1's When we seek minimal expression, So, No need covering all the Don't cares.

3. As @MKUtkarsh mentioned, **NOTE that When Don't cares are involved, We get a class of Functions, Not a Specific Function. So, Unless things like Minimal expression, Minimal EPI etc are asked, We can even say that $AC' + CA'$ is also a Correct SOP for this K-Map. Since there are $5$ Don't Cares, We can have $2^5$ functions for this K-Map. Among which the Minimal SOP would be $A'C$.**

Credit : @MKUtkarsh

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