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+11 votes
901 views

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

asked in Digital Logic by Veteran (59.6k points)
edited by | 901 views
+1
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

4 Answers

+14 votes
Best answer
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.
answered by Loyal (9.1k points)
edited by
0
You missed an entry AB'C'
0
A'B'C' + A'B C' + ABC = A'C'(B' + B) + ABC = A'C' + ABC
+1
The given K-map has an entry B'C'. So, when you expand with A, it must be AB'C' + A'B'C'.
0
I agree I'll edit the answer

finally it comes out as ABC + B'C' + A'C'
0
@Arjun sir is this ans correct?
0
how we can  expand this K map of 2 variables (4 cells) to K map of three variable (8 cells)?????
0
how to convert 2 variable k map to 4 variable k map?
+14 votes
B'C'+ BC'A'+ ABC = C'(B' + BA') + ABC = C'(A'+ B') + ABC = A'C'+ B'C'+ ABC
answered by Veteran (363k points)
edited by
0
sir, this is variable entrant map??? right
+3 votes

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)

answered by (421 points)
0 votes
(b!c!) +ab +ac!        ?
answered by (391 points)

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