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Simplified Boolean expression for A'BC+AB'C'+A'B'C'+AB'C+ABC

A . AB

B . B'C

C . AB+(A'+AB')C

D . AB'+BC+B'C'

in Digital Logic by Boss (45.2k points)
edited by | 15.1k views
0
Option (D) is correct answer

5 Answers

+6 votes
Best answer

A' BC + AB'C' + A'B'C' + AB'C + ABC

=A' BC + AB'C' +  AB'C' + A'B'C' + AB'C + ABC                      (AB'C' =  AB'C 'AB'C ') 

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

=BC ( A' + A ) + B'C' ( A' + A ) + AB'( C' + C )

=BC + B'C' + AB'

Hence,Option(D) AB' + BC + B'C' is the correct choice.

by Boss (41k points)
selected by
+3
According to me , no need to solve manually.
simply using truth table we can find minterms and draw a k-map.
correct me if i am wrong @leenSharma sir
+1
Thanks Leen sharma .
0
yes, you can solve it by k-map too.By K-map we can solve boolean expression easily .I wanted to show him steps that's why i did in that way.
0
okay ! please check my solution , i also upload with k-map figure
please check
+1

Devwritt Your solution is also right.

0
thanks
+2 votes
D option is correct ans

A'BC +AB'C'+A'B'C'+ AB'C+ ABC

A'BC+B'C'(1)+AB'C+ ABC

A'BC+B'(C'+AC)+ABC

BC (A'+A)+B'(C'+A)

BC(1)+B'(C'+A)

BC+ B'C'+ B'A
by Boss (19.9k points)
edited by
0
Can you derive option D from this ?  please write it how ...because i tried but haven't got anything.
0
check my solution.
0
you have derived it from wrong question there is a term in it which is A'B'C' and you did not use it .
0
Ary yaar bi mistake i have missed that term . But my approach is correct !
0

okay then tell me In 4th line from B'(C'+AC)   how did you write  B'(C'+A)

0

 B'(C'+AC) = B'(C'+C ) (C'+A)  = B'(C'+A)

+1
see if we have a+a'b just simply cut the a' literal from a'b term so we will get a+b hence a+a'b is equivalent to a+b :) rt ?
+1
I got stuck in this step for last 2 hour before you solved it .I don't know what i was doing wrong...i solved it 4-5 times..now i have resolved in my way and i got the answer thanks again.
+1
got it now .i was doing very silly mistake .
0
the above shortcut that i told is very useful in such type of question :)
+2 votes

ANSWER: OPTION D
using K-map
 

by Active (4k points)
0
As a is most significant bit in the case of what you have taken here most significant should be taken in the place of c the above is not correct  thing u have done according to me correct me of iam going wrong
0

@Vishal , Its not always true that Most significan bit should be in place of variable C . Point is final output must be valid and correct . So you can do in both way, you can use this way(attached fig) and you'll get the same output . But its good thing Vishal, you can remind and use only one method . But in exam you can't say they will follow your method , right?? So, .focus on basics.

0 votes
option D
by Active (1.3k points)
0 votes
using k map (d) is correct option.
by (71 points)

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