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QUESTION: 1

Consider the following Boolean function of four variables:

The function is

Solution:

The K-map would be

So, the minimized expression would

be x'z + xz'.

So, option B.

QUESTION: 2

Consider the following Boolean function of four variables

The function is

Solution:

QUESTION: 3

The simplified SOP (Sum of Product) from the Boolean expression

1s

Solution:

QUESTION: 4

Consider the 4-to-1 multiplexer with two select lines S_{1} and S_{0} given below

The minimal sum-of-products form of the Boolean expression for the output F of the multiplexer is

Solution:

S0 and S1 are used to select the input given to be given as output.

QUESTION: 5

Consider the following Boolean expression for F:

The minimal sum of products form of F is

Solution:

Hence, option A is correct.

QUESTION: 6

Consider the following minterm expression F for :

The minterms 2, 7, 8 and 13 are 'do not care' terms. The minimal sum-of-products form for F is

Solution:

While putting the terms to K-map the 3rd and 4th columns are swapped so do 3rd and 4th rows. So, term 2 is going to (0,3) column instead of (0,2), 8 is going to (3,0) instead of (2,0) etc..

Solving this k-map gives B) as the answer.

QUESTION: 7

Consider the two cascade 2 to 1 multiplexers as shown in the figure .

The minimal sum of products form of the output X is

Solution:

QUESTION: 8

The output F of the below multiplexer circuit can be represented by

Solution:

QUESTION: 9

A multiplexer with a 4 - bit data select input is a

Solution:

for n bit data select input

QUESTION: 10

It is possible for an enable or strobe input to undergo an expansion of two or more MUX ICs to the digital multiplexer with the proficiency of large number of

Solution:

It is possible for an enable or strobe input to undergo an expansion of two or more MUX ICs to the digital multiplexer with the proficiency of large number of inputs.

QUESTION: 11

Consider a multiplexer with X and Y as data inputs and Z the as control input. Z = 0 selects input X, and Z = 1 selects input Y. What are the connections required to realize the 2-variable Boolean function F = T + R, without using any additional hardware?

Solution:

Z'X + ZY..

Put Z = T, X = R, Y = 1 in Z'X + ZY..

= T'R + 1*T

= (T+T') (T+R)

= T + R

QUESTION: 12

The circuit shown below implements a 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?

Solution:

QUESTION: 13

Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of variables.

What is the minimum size of the multiplexer needed?

Solution:

2^{n - 1}

We will map variables to select lines and variable to input line

QUESTION: 14

The following circuit implements a two-input AND gate using two 2-1 multiplexers.

What are the values of X1,X2,X3?

Solution:

F = (bX1' + aX1)X3 + X2X3'

Put X_{1} = b, X_{2} = 0, X_{3} = a to get F = ab.

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