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Consider the following multiplexer where $10, 11, 12, 13$ are four data input lines selected by two address line combinations $A1A0=00,01,10,11$ respectively and $f$ is the output of the multiplexor. EN is the Enable input.

The function $f(x,y,z)$ implemented by the above circuit is 

  1. $xyz'$
  2. $xy + z$
  3. $x + y$
  4. None of the above
asked in Digital Logic by Veteran (59.6k points)
edited by | 2.4k views
+2
Incomplete figure.Please someone edit it.
+5

Here is full image.

0
It could be done via Table and K-map but that will be more time consuming.

1 Answer

+38 votes
Best answer
As $X$ connected to $I0$  & $I1$, $Y$ connected to $I2,$ $Y'$ connected to $I3$ & $A1,$ $Z$ connected to $A0$ and $Z'$ connected to ENABLE (EN),

$F= ( {\overline{A1}}.{\overline{A0}}.I0+ {\overline{A1}}.A0.I1 +A1.{\overline{A0}}.I2 + A1.A0.I3 ).EN$

$\implies F = (XYZ' +XYZ + Y'Z'Y + ZY')Z'$
$\qquad= (XYZ' +XYZ + ZY')Z' =XYZ'$
answered by Veteran (55.6k points)
edited by
+2

how to simply this:

F = (XYZ' +XYZ + Y'ZY + ZY')Z'

= (XYZ' +XYZ + ZY')Z'  //this step to final step XYZ'

=XYZ'

0
z*z' =0
+1
@karthik

  (XYZ' +XYZ + Y'ZY + ZY')Z'

=XYZ'Z'+XYZZ'+Y'ZYZ' + ZY'Z'

=XYZ'+0+0+0

=XYZ'
0
Where is X,Y,Z in the circuit diagram?
0

why is EN  multiplied in characteristic equation? Kindly explain . Thanks

+1

yes it will multiply

When EN = 1, themultiplexer performs its operation depending on the selection line

0

Thanks :)

+1
in the above question enable will be in complemented form
0

enabled at  0 and disabled at 1?

+1
yes for the above circuit because inverter is present there
+1

As you mentioned - "Z is connected to A"

then how could you substitute A0as Z for the third min-term.

It should be Y'Z'Y instead of Y'ZY.

Correct me if I am wrong. Although I know that it won't affect the final answer by doing so.

0
how you write this function in xyz form from A1, A0??????????
0
@raj see in circuit...  A1 is getting y' and AO is getting z..
0

@gari thank u

0

how we know "X connected to I0  I1 .Y connected to I2  "

0
I think u should look at the diagram carefully
0
This is totally due to depression .. thanks @akanshadewangan24
0
I want to know, why you multiply enable with the all the input ??

What the reason for that ?
Answer:

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