K-map and don't cares

Question

"once you have assumed a don't care as '1' u can't use the same don't care for grouping zeros and vice versa."

is it correct or not??

Comments

First you fix the notation which you want ( either POS or SOP )

then fix the Don't care term as per your requirement

 

When you have don't care terms in your function,

Free variables and Prime Implicant  may differ to POS and SOP forms

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Your reply is not according to my question.

But my doubt become clear now.  The confusion come from this question-

https://gateoverflow.in/936/gate2003-45

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that is actually two questions, they separately ask the sop and pos form literals...

ON SOLVING FOR SOP :-

Fix the don't care terms to 1 which you want, neglect remaining and now form the boolean expression

ON SOLVING FOR POS :-

Fix the don't care terms to 0 which you want, neglect remaining and now form the boolean expression

this is i explained in my previous comment.

 

Your reply is not according to my question.

When you have don't care terms in your function,
Free variables and Prime Implicant  may differ to POS and SOP forms

this is extra information i provided.... this is the consequence of the don't care terms

 

 

But my doubt become clear now.

OK

Answer 1

PS: Some wrong beliefs about don't cares

1. "once you have assumed a don't care as '1' u can't use the same don't care for grouping zeros and vice versa"
2. "if don't care has been used in POS than can't be used in SOP"

Both these statements are wrong. Don't care simply means just don't care -- say we use don't care d3d3 for grouping 11 in SOP we can use d3d3 for grouping 0 in POS. (The literals in SOP and POS may not be the same) 

 

Comments

if a function has don't cares then it can be represented as many functions which results the same.
Let F is a function which contains some don't cares. Let f1 abd f2 be minimal sop and pos which represents the same function F
Then f1 is not equivalent to f2 if
Same don't care(s) is used for minimal sop as well as for minimal pos.
f1 and f2 are equivalent if
they contain different don't cares for calculation.

In both the cases f1 and f2 represents the function F but they might not be same.