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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?

in Digital Logic by Loyal (8.4k points) | 129 views
$ac^{'} + a^{'}c$
No need covering the Don't cares from which you got $C'A$
ok thanks but it's not wrong i believe
Yes. Nothing wrong unless asked Minimal expression etc. When Don't cares are involved, We get a class of Functions, Not a Specific Function.

Nice Point. Will include in my answer. Thank you for mentioning.

3 Answers

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Best answer

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

by Boss (27.3k points)
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Thank You.
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The answer for this will be a'c, as the other don't care don't have any inpact on sop , so only one quardant will be form.

by (115 points)
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we try to make large subcube  and cover all one's.

by Boss (36.5k points)
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