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+9 votes
580 views

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

asked in Digital Logic by Veteran (68.8k points) | 580 views
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

+11 votes
Best answer
answer - ABC + B'C' + A'C' [EDIT]

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 Boss (9.3k points)
selected by
You missed an entry AB'C'
A'B'C' + A'B C' + ABC = A'C'(B' + B) + ABC = A'C' + ABC
The given K-map has an entry B'C'. So, when you expand with A, it must be AB'C' + A'B'C'.
I agree I'll edit the answer

finally it comes out as ABC + B'C' + A'C'
@Arjun sir is this ans correct?
how we can  expand this K map of 2 variables (4 cells) to K map of three variable (8 cells)?????
+8 votes
B!C! + BC!A! + ABC = C!(B! + BA!) + ABC = C!(A! + B!) + ABC = A!C! + B!C! + ABC
answered by Veteran (332k points)
sir, this is variable entrant map??? right
+1 vote

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 (249 points)
0 votes
(b!c!) +ab +ac!        ?
answered by (401 points)


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