in Digital Logic retagged by
5,110 views
22 votes
22 votes

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

in Digital Logic retagged by
5.1k views

2 Comments

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
5
5
i dont get this K-map
0
0

4 Answers

26 votes
26 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.
edited by

4 Comments

make a characteristic table for 3 variables and check all 8 combinations, if L.H.S. matches R.H.S for every combination then it is valid else not.
0
0

@CSHuB

No it is wrong.

(BC)’ = B’ + C’ .

i.e.  A’ (BC + (BC)’ )

     =>  A’ (BC + B’ + C’) 

     = > A’

 

To verify draw the truth table.

1
1

Resultant K-map

Resultant Kmap

0
0
29 votes
29 votes
B'C'+ BC'A'+ ABC = C'(B' + BA') + ABC = C'(A'+ B') + ABC = A'C'+ B'C'+ ABC
edited by
by

2 Comments

sir, this is variable entrant map??? right
2
2
Yes, this is directly from variable entrant map.
0
0
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:

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

                                               $\downarrow$

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

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

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

$f= ABC+A’C’+B’C’$

edited by

2 Comments

@ Kushagra gupta sir,we need to minimize this expression into : ABC+B’C’+A’C’
0
0
@ Kushagra gupta sir,we need to minimize this expression into as below :

A’B’C’+A’BC’+AB’C’+ABC

=A’C’(B’+B)+AB’C’+ABC

= A’C’+AB’C’+ABC

= C’(A’+AB’)+ABC

= C’(A+A’)(A’+B’)+ABC

= C’(A’+B’)+ABC

= ABC+A’C’+B’C’
1
1

Related questions