The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of $\left(xy+xz'\right)$ is $4.$ What are the minimum possible literal counts of the product-of-sum and sum-of-product representations respectively of the function given by the following Karnaugh map? Here, $X$ denotes "don't care"
this is what i have done, plz tell me where i was wrong.
pink ink is for SOP = 2 + 3 + 3 = 8
blue ink is for POS = 2 + 2 + 2 + 3 = 9
We will be getting two different grouping..
Grouping $1: (9,8)$
GROUPING $2: (9,10)$
Both the grouping are correct representation of the function $f(wxyz)$
PS: Some wrong beliefs about don't cares
Both these statements are wrong. Don't care simply means just don't care -- say we use don't care $d3$ for grouping $1$ in SOP we can use $d3$ for grouping 0 in POS. (The literals in SOP and POS may not be the same)
K-Map grouping is not unique. And the question says about minimal literals. So, the best answer would be (9,8) Since there is no option in GATE we can go with $(9,10)$ (the question setter might have missed Grouping 1)
Is it correct or in correct please clarify ..
POS: $\left ( x+w+z \right )\left ( z'+w' \right )\left ( x'+w' \right )\left ( y'+z' \right )$
I am getting (9,8), 9 for POS and 8 for SOP.
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.
@Pooja Palod We can write SOP using 8 literal as well:
y'w'+xyz'+x'z'w which is minimal and even in question it is mentioned that "What are the minimum possible literal counts of the product-of-sum and sum-of-product representations".
so, Answer should be (9,8) as it is minimum possible.
@Arjun Sir please look this question.
Correct me if I am wrong.
I am getting 9 pos and 9 sop...
I am getting 9 pos and 9 sop..
And once I hv used a dont care as 0. Thn I havnt used the sam dont care as 1.