UGC NET CSE | June 2012 | Part 3 | Question: 53

Question

Consider the below circuit and find the output function f(x, y, z)

• A. $x \bar{z} + xy + \bar{y}z$
• B. $x \bar{z} + xy + \bar{y} \bar{z}$
• C. $xz + xy + \bar{y} \bar{z}$
• D. $xz + x \bar{y} + \bar{y}z$

Answer 1

Answer : A

Lets consider 1st Mux

select line is given as Z

if we consider Z(Select Line) as 1 then input line is going to be selected as 1 a/c to given Mux diagram which is y'

if we consider Z(Select Line) as 0 then input line is going to be selected as 0 a/c to given Mux diagram which is x

Let say output of 1st Mux is A = y'z + xz'

Now Lets consider 2nd Mux

if we consider Y(Select Line) as 1 then input line is going to be selected as 1 a/c to given Mux diagram which is x

if we consider Y(Select Line) as 0 then input line is going to be selected as 0 a/c to given Mux diagram which is y'z + xz'

xy + y'(xz'+y'z)

xy + xy'z' + y'z

y'z + x( y+ z')

xy + xz' + y'z

Comments

xy + y'(xz'+y'z)

after this line

xy +( xy'z' + y'y'z) --how to solve this,please explain.I am not able to solve it

 

xy + xy'z' + y'z

y'z + x( y+ z')

xy + xz' + y'z

Answer 2

output of mux 1=(XZ'+Y'Z)

OUT PUT OH MUX 2=

(XZ'+Y'Z)Y'+XY

=XZ'Y'+Y'Z+XY

==X(Z'Y'+Y)+Y'Z

==X(Y+Z')+Y'Z

==XY+XZ'+Y'Z(OPTION A)¯¯

Comments

In 4 the step y' is not present how.?

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@ Hemavasu

Law of distribution applied in Step 4