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The Boolean function in sum of products form where K-map is given below (figure) is _______

edited | 901 views
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simple approach:

1) just draw truth table for 3 variables(0 to 7)

2) now set function value acoording to given kmap

3) minimize function now using kmap

Answer - $ABC + B'C' + A'C'$

Expand this $K$ map of $2$ variables $($$4 cells) to K map of three variable ($$8$ cells$)$

Entries which are non zero are: $A'B'C', AB'C', A'BC'$ and $ABC$

Minimize $SOP$ expression using that $K$ map.
edited
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You missed an entry AB'C'
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A'B'C' + A'B C' + ABC = A'C'(B' + B) + ABC = A'C' + ABC
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The given K-map has an entry B'C'. So, when you expand with A, it must be AB'C' + A'B'C'.
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I agree I'll edit the answer

finally it comes out as ABC + B'C' + A'C'
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@Arjun sir is this ans correct?
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how we can  expand this K map of 2 variables (4 cells) to K map of three variable (8 cells)?????
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how to convert 2 variable k map to 4 variable k map?
B'C'+ BC'A'+ ABC = C'(B' + BA') + ABC = C'(A'+ B') + ABC = A'C'+ B'C'+ ABC
edited by
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sir, this is variable entrant map??? right

Alternate Method:-

 C B 0 1 0 1 0 1 A’ A

Step1: (Mark all the variables in Cell as 0)

 C B 0 1 0 1 0 1 0 0

f0=B’C’  ---- i

Step2:  Minterm for variable A’. (Mark minterm obtained for 1 as Don’t Care and target variable as 1)

 C B 0 1 0 X 0 1 1 0

fA’=A’C’ --- ii

Step2:  Minterm for variable A. (Mark minterm obtained for 1 as Don’t Care and target variable as 1)

 C B 0 1 0 X 0 1 0 1

fA=ABC ---iii

f=ABC+A’C’+B’C’ (Ans)

(b!c!) +ab +ac!        ?

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