Logic Gates Multiple Choice Question And Answers

Logic Gates

Question 1. The logic gate represented in the adjoining figure is

1. An OR gate
2. A NOT gate
3. A NAND gate
4. An XOR gate

Answer: 1. An OR gate

The output of the combination of the two given gates represents an OR gate.

G₁ is a NOR gate, which gives the output \(Y^{\prime}=\overline{A+B}\).

Two identical inputs in a NOR gate give the same output as a NOT gate.

Thus, \(\bar{Y}=\overline{Y^{\prime}}=\overline{\overline{A+B}}\) = A + B.

Hence, it is an OR gate.

The truth table for this gate is as under.

This output corresponds to an OR gate.

Question 2. The given combination of gates is equivalent to

1. An AND gate
2. An OR gate
3. A NOR gate
4. A NOT gate

Answer: 3. A NOR gate

The output of the combination of the given gates (G₁ and G₂) with a NOT gate is the same as that of a NOR gate.

The output of G₁ (a NOR gate) is \(Y^{\prime}=\overline{A+B}\).

The G₂ gate is equivalent to a NOT gate.

Hence, \(Y^{\prime \prime}=\overline{Y^{\prime}}=\overline{\overline{A+B}}\) = A + B.

Finally, through a NOT gate, \(Y=\overline{A+B}\), which is the output of a NOR gate. This is also indicated by the following truth table.

The output corresponds to that of a NOR gate.

Question 3. Which logic gate is represented by the given combination of logic gates?

1. OR
2. NAND
3. AND
4. NOR

Answer: 3. AND

The truth table for the given combination of gates is shown below. In the given circuit, there are two NOT gates whose outputs Y₁ and Y₂ are complements of A and B. These inputs to the given NOR gate give the final output Y as that of an AND gate.

The truth table shows that when both the inputs are high then only we are getting a high value of the output, otherwise zero. This corresponds to an AND gate.

Question 4. The output in the given circuit is

1. (A + B).\(\bar{B}\)
2. (A.B).\(\bar{B}\)
3. (A + B).B
4. (A.B) + B

Answer: 1. (A + B).\(\bar{B}\)

The output Y’ of the OR gate. G₁ is Y’ = A + B and the output of G₂ is \(\bar{B}\). G₃ is an AND gate whose output is

\(Y=Y^{\prime} \cdot B=(A+B) \cdot \bar{B}\)

Question 5. The symbolic representations of four logic gates are shown below.

Pick out the combination that represents the symbols for the AND, NAND, and NOT gates respectively.

1. (3), (2), and (1)
2. (2), (4), and (3)
3. (3), (2), and (4)
4. (2), (3), and (4)

Answer: 3. (3), (2), and (4)

The symbols given in the question are for the

1. OR,
2. AND,
3. NOT and
4. NAND gates

Question 6. The circuit given here is equivalent to

1. An AND gate
2. A NAND gate
3. A NOR gate
4. A OR gate

Answer: 3. A NOR gate

The output of the (NOR gate) G₁ is \(Y^{\prime}=\overline{A+B}\)

The output of the (NAND gate) G₂ is Y” = \(Y^{\prime \prime}=\overline{Y^{\prime}}=\overline{A+B}=A+B\)

The output of the (NOT gate) G₃ is Y = Y” = A + B.

This final output corresponds to a NOR gate, which is confirmed by the truth table given below.

Question 7. To get an output of 1 for the following circuit, the correct choice for the inputs is

1. A = 1, B = 0, C = 0
2. A = 1, B = 1, C = 0
3. A = 1, B = 0, C = 1
4. A = 0, B = 1, C = 0

Answer: 3. A = 1, B = 0, C = 1

The output of G₁ (an OR gate) is Y’ = A + B.

The output Y of G₂ (an AND gate) is Y = (A + B).C

For Y =1, we have C = 1, and either A = 0 and B =1 or A =1 and B = 0 or A = 1 and B = 1.

Hence, option (3) gives a correct combination.

Question 8. What are the respective values of the output Y in the given circuit when all three inputs (A, B, C) are first 0 and then 1?

1. 0 and 1
2. 0 and 0
3. 1 and 0
4. 1 and 1

Answer: 3. 1 and 0

The output of the AND gate G₁ is Y’ = A.B

The output of the NAND gate G₂ is \(Y=\overline{Y^{\prime} \cdot C}=\overline{(A \cdot B) \cdot C}\)

If A = B = C = 0 then Y = \(\bar{0}\) = 1.

If A = B = C =1 then Y = \(\bar{1}\) = 0.

This can be shown by the truth table given below.

Question 9. The output Y in the logic circuit shown in the figure will be

1. \(Y=\bar{A} \cdot \bar{B}\)
2. \(Y=\overline{A \cdot B}\)
3. Y = A.B
4. Y = \(Y=\overline{A+B}\)

Answer: 3. Y = A.B

In the given circuit, G₁ is a NAND gate and G₂ acts as a NOT gate.

⇒ \(Y^{\prime}=\overline{A \cdot B}\)

and \(Y=\overline{Y^{\prime}}=\overline{\overline{A \cdot B}}=A \cdot B\) → (1)

Now, (1) is the Boolean expression for an AND gate.

Question 10. In the given circuit, the values of the output Y for all possible inputs A and B are expressed by the truth table

Answer: 4.

In the given diagram, G₁ represents a NOR gate and G₂ is effectively NOT gate.

The output of G₁ is \(Y^{\prime}=\overline{A+B}\) and the final output is \(Y=\overline{Y^{\prime}}=\overline{\overline{A+B}}=A+B\) which represents the Boolean expression for an OR gate. The truth table is given below.

This corresponds to the option (4).

Question 11. The diagram shown in the adjoining figure performs the logic operation of a/an

1. OR gate
2. AND gate
3. XOR gate
4. NAND gate

Answer: 2. AND gate

Gx is a NAND gate whose output is \(Y^{\prime}=\overline{A \cdot B}\).

A NAND gate with one input is equivalent to a NOT gate. Thus, the final output is \(Y=\overline{Y^{\prime}}=\overline{\overline{A \cdot B}}\) = A.B, which is the Boolean expression for an AND gate.

Thus, the given combination of gates performs the logic operation of an AND gate.

Question 12. Which of the following gates will have an output of 1?

1. 1
2. 2
3. 3
4. 4

Answer: 2. 2

1. Is a NAND gate with the output Y = \(\overline{1 \cdot 1}=\overline{1}\) = 0.
2. Is a NAND gate with the output Y = \(\overline{0 \cdot 1}=\overline{0}\) = 1.
3. Is a NOR gate with the output Y = \(\overline{1+1}=\overline{1}\) = 0.
4. Is an XOR gate with the output Y = 0.

Thus, only (2) will give an output of 1.

Question 13. The given figure shows a logic operation with two inputs A and B and the output C. The voltage waveforms across A, B, and C are as given. The logic circuit represents a/an

1. NOR gate
2. AND gate
3. OR gate
4. NAND gate

Answer: 3. OR gate

The values of the inputs A and B and the output C as given in waveforms are shown in the following table.

The values of the output C indicate that the logic circuit represents an OR gate.

Question 14. The adjoining figure shows a logic circuit with two inputs A and B and the output Y. The voltage waveforms of A, B, and Y are given in the figure. The logic circuit represents

1. A NOR gate
2. An OR gate
3. A NAND gate
4. An AND gate

Answer: 3. A NAND gate

The values of the inputs A and B and the output Y at different time intervals are shown in the following table.

The values of the output Y indicates that the. logic operation is of a NAND gate.

Question 15. The figure given here shows a logic circuit with two inputs A and B and the output C. The voltage waveforms of A, B, and C are shown in the figure. The logic circuit is for a/an

1. AND gate
2. NAND gate
3. OR gate
4. NOR gate

Answer: 1. AND gate

The values of the inputs A and B and the output C at different time intervals are shown below in a tabular form.

The values of the output C correspond to the logic operation of an AND gate.

Question 16. The correct Boolean operation represented by the circuit diagram shown is

1. AND
2. OR
3. NAND
4. NOR

Answer: 3. NAND

According to the given logic circuit, the LED will glow when both A and B are OFF (A = B = 0) or when either A or B is OFF.

The LED will not glow when it is short-circuited by closing both A and B (A = B = 1).

This is expressed in the following truth table, which gives the Boolean expression \(Y=\overline{A \cdot B}\) corresponding to a NAND gate.

Question 17. The truth table for the circuit given in the adjoining figure is

Answer: 2.

Let Y₁ be the output of the given OR gate. With Y₁ and A as the inputs in the NAND gate, the circuit produces the final output Y as shown in the following truth table.

Question 18. To get an output of 1 at R in the given logic circuit, the input values must be

1. X = 0 and Y = 0
2. X = 1 and Y = 0
3. X = 1 and Y = 1
4. X = 0 and Y = 1

Answer: 2.

The given logic circuit can be redrawn as shown in the given figure. The final output R is obtained as given in the truth table shown below.

Thus, to get an output of 1 at R, the values of the inputs must be X =1 and y = 0.

Question 19. The output of the given combination of logic gates is

1. \(A \cdot \bar{B}\)
2. \(\bar{A} \cdot B\)
3. A.B + \(\overline{A \cdot B}\)
4. \(A \cdot \bar{B}+\bar{A} \cdot B\)

Answer: 1. \(A \cdot \bar{B}\)

The logic circuit has been redrawn as shown here. The corresponding truth table is shown below.

This output Y is the same as that produced by the \(A \cdot \bar{B}\) gate shown below.

Hence, the given circuit corresponds to the Boolean expression \(Y=A \cdot \bar{B}\).

Question 20. The given logic circuit is equivalent to a/an

1. AND gate
2. NOR gate
3. NANDgate
4. OR gate

Answer: 4. OR gate

The truth table for the given logic circuit is shown below.

The output Y corresponds to an OR gate. Thus, the given logic circuit represents an OR gate.

Note: Y = \(\bar{A} \cdot \bar{B}\) = A + B

Question 21. The output of the given combination of gates is equivalent to a/an

1. AND gate
2. OR gate
3. NOR gate
4. NAND gate

Answer: 1. AND gate

The symbol acts as a NOT gate.

Hence, the Boolean expression for the output will be

∴\(\overline{(\overline{A+A})+(\overline{B+B})+(\overline{C+C})}=\overline{\bar{A}+\bar{B}+\bar{C}}=A \cdot B \cdot C\)

Hence, the given combination of gates is equivalent to an AND gate.

Question 22. The figure given below shows a logic circuit with two input signals A and B.

The output signal y is given by the graph

Answer: 3.

For the given logic gate, Y = \(\overline{\bar{A} \cdot \bar{B}}\) = A + B.

The truth table and the corresponding output are given below. The circuit is equivalent to an OR gate.

Question 23. For the given logic circuit, the truth table is

Answer: 4.

The output Y for the given logic circuit corresponds to an AND gate, whose truth table is given in option (4). This can be seen in the following table.