Test: Boolean Algebra & Logic Gates- 2

QUESTION: 1

The function

can be written as

A.
B.
C.
A
D.
None of these

Solution:

QUESTION: 2

The Karnaugh map for the Boolean function F of 4 Boolean variables is given below where A, B, C are don't care conditions. What values of A, B, C will result in the minimal expression?

A.
A = B = C = 1
B.
B = C = 1 ; A = 0
C.
A = C= 1; B = 0
D.
A = B = 1; C = 0

Solution:

From the given k-map we can observe that B = 1 always. Also if A is to be paired than it should be
1. If A is selected there is no need to take C.
Hence, A - 1, B = 1, C = 0 Hence option (d) is correct

QUESTION: 3

Let f(A, B) = then simplified from of the function

A.
B.
C.
D.
None of these

Solution:

QUESTION: 4

Consider the circuit-shown below. Each of the control inputs, C₀ through C₃, must be tied to a constant, either ‘0’ or '1'.

What are the values of C₀ through C₃ that would cause F to be the exclusive OR of A and B?

A.
(1 ,0, 0 ,1 )
B.
( 0 ,1 ,1 ,1 )
C.
(0, 1,1,0)
D.
(1,1, 1,1)

Solution:

The output of

QUESTION: 5

Write the minimized expression of the function of three variables that is 1 if the third variable is equal to the OR of the first two variable, 0 otherwise

A.
(x+y)+z
B.
C.
D.

Solution:

Constructing the table we have

Hence the required expression is

QUESTION: 6

Which of the following functions implements the Karnaugh map shown below?

A.
B.
D ( C + A )
C.
D.

Solution:

Solving the given K-map we have

Hence (b) is correct option

QUESTION: 7

The Boolean expression for the shaded area in the given Venn diagram is

A.
B.
C.
D.

Solution:

Hence, the required boolean expression is

Hence (b) is the required option.

QUESTION: 8

The Boolean expression is a simplified version of expression:

Then which of the following choice is correct:
1. Don’t care conditions don’t exist.
2. Don’t care conditions exist.
3. D (16, 18, 20, 23, 27, 29) is the set of don’t care conditions.
4. D (16, 20, 22, 27, 29) is the set of don’t care conditions.

A.
1 only
B.
2 and 3 only
C.
2 and 4 only
D.
Data insufficient

Solution:

Only (c) option satisfies the required condition.

QUESTION: 9

The logical expression for K-Map shown above is:

A.
B.
C.
D.

Solution:

QUESTION: 10

The Boolean expression for the shaded area in the Venn diagram is

A.
B.
C.
D.
None of these

Solution:

QUESTION: 11

Consider, a four variable Boolean function, which contains half the number of minterms with odd number of 1 ’s. Then the Boolean can be realized with variables A, B, C, D as: