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5,144 views
22 votes
22 votes

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

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4 Answers

Best answer
26 votes
26 votes
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 by
29 votes
29 votes
B'C'+ BC'A'+ ABC = C'(B' + BA') + ABC = C'(A'+ B') + ABC = A'C'+ B'C'+ ABC
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7 votes
7 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)

6 votes
6 votes

Variable Entered Map:

$B$ $C$ $f$
$0$ $0$ $1$
$0$ $1$ $0$
$1$ $0$ $A'$
$1$ $1$ $A$

                                               $\downarrow$

$A$ $B$ $C$ $f$
$0$ $0$ $0$ $1$
$0$ $0$ $1$ $0$
$0$ $1$ $0$ $1$
$0$ $1$ $1$ $0$
$1$ $0$ $0$ $1$
$1$ $0$ $1$ $0$
$1$ $1$ $0$ $0$
$1$ $1$ $1$ $1$

$f=\Sigma (0,2,4,7)$

$f=A'B'C'+A'BC'+AB'C'+ABC$

$f= ABC+A’C’+B’C’$

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