Question

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'

Comments

Option (D) is correct answer

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But I got B'C'+AC+BC

Answer 1

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.

Comments

thanks

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why did u duplicate this ? AB'C' + AB'C' can u explin which rule u used?

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AB’C’ is duplicated and the reason is that to find the common terms and minimize it.
See these 4 terms : A'B'C' +  AB'C' + AB'C' + AB'C.

In this, A'B'C' +  AB'C’ :  B’C’ is common

and  AB'C' + AB'C :  AB’ is common.

So, A'B'C' +  AB'C' + AB'C' + AB'C = B’C’ + AB’.

Now come to the property or rule: Idempotent rule is used here
Idempotent rule says : A + A = A  and A.A =A

Answer 2

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

Comments

got it now .i was doing very silly mistake .

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the above shortcut that i told is very useful in such type of question :)

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Please tell me how it get

Answer 3

ANSWER: OPTION D
using K-map
 

Comments

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

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@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.

Answer 4

using k map (d) is correct option.