Multiplexer

Question

Consider the given function F(A,B,C,D) = Σm(2,3,5,6,8,9,11,14) then what is the value connected at input I1 in the figure shown below if the select lines are connected to B & D respectively? 

 

 

Comments

A+C ??

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For every question shall we comment to add the source of the question?

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A'C+AC'+AC=A+C=I1

Answer 1

input of I1 is a+c.

Answer 2

Input I1 -> B=0 , D=1(select lines)

Consider all remaining cases for A, C

A=0, C=0 ->  m1( not satisfiable)

A=0 C=1 ->  m3(satisfiable)

A=1 C=0 ->  m9(satisfiable)

A=1 C=1 ->m11(satisfiable)

The value A + C satisfies these conditions, and this should be  the input connected to  I1.

Comments

Can you elaborate, it's confusing

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1. You have asked for input I1, as B,D are select lines then to select I1, the values of B D should be 0 1

2.If you fix B D values as 0 1 then other possible no.of combinations for A C are 4(00,01,10,11), which i have listed in my answer.

3.If I enumerate all the possiblilities, I will have following min terms,

  A B C D

  0 0 0 1

  0 0 1 1

  1 0 0 1

  1 0 1 1

If you see B D values are always  0 1.

4.Possible min terms are m1,m3,m9,m11 of which only m1(A=0,C=0) is not satisfied by the given expression. Now you need to connect A C to I1 in such a way that it should turn true for all combinations expect(A=0,C=0), You can easily observe that we can use OR function between them, as it is only false when both are false.

5.Hence Input connected should be A+C.

Hope this clears your confusion.

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Yea,now it's clear.