GATE IT 2005 | Question: 48

Question

The circuit shown below implements a $\text{2-input}$ NOR gate using two $2-4$ MUX (control signal $1$ selects the upper input). What are the values of signals $x, y$ and $z$?

 

• A. $1, 0, B$
• B. $1, 0, A$
• C. $0, 1, B$
• D. $0, 1, A$

Comments

Why does question says

2−4 MUX,it uses 1-2 MUX ?

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Sometimes multiplexers are grouped together, such that one might have a chip with two groups of four inputs and two outputs; one input from the first group is forwarded to the first output, and one from the second group is sent to the second output.

i think this is what might comfort us for the above query in the question.

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If you take option A then also we get the same output as:

(B’A+B)’ = A’.B’

Answer 1

$f = Az+B\bar z$ (As $A$ will be selected when $z$ is high) . 

So, next function will become $g = xf +y\bar f$ 

$ = x\left(Az+B \bar z \right) + y (\overline {Az+B \bar z})$

Putting $x = 0, y = 1, z = A$, we get $g = \overline {AA+B \bar A} = \overline {A + B} \: \left( \because A + B\bar A = A + B \right)$ and answer will become D

Comments

x=0 y=1 z=$\bar{B}$ is also a solution :)

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Why option C  is not correct?

If Z=B then AB will be select input for next mux then y= 1 and x=0 we will get right answer

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OPTION C will give us NAND

Answer 2

Instead of finding a function 'f' for the first MUX (in terms of z,x and y) and the second MUX (in terms of f , x and y), we can logically find out the answer.We can put in 4 values of A and B and analyse the output C. We can get the values appropriate values of x and y by drawing and comparing with a 2x1 MUX when A and B are given as inputs respectively.

Answer 3

Let the lower mux function be f=Az'+Bz Upper mux g=xf'+yf Now put option a in function g it comes out to be a'b' which is (a+b)'

Comments

Z = B, means Z should be selecting B input rt?

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I dont know much about mux ,i just did a solution using the function of a mux.

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Probably you are right..

Answer 4

ans should b D.