## Logic Gates

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

- An OR gate
- A NOT gate
- A NAND gate
- An XOR gate

**Answer:** 1. An OR gate

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

G_{1} 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**

- An AND gate
- An OR gate
- A NOR gate
- A NOT gate

**Answer:** 3. A NOR gate

The output of the combination of the given gates (G_{1} and G_{2}) with a NOT gate is the same as that of a NOR gate.

The output of G_{1} (a NOR gate) is \(Y^{\prime}=\overline{A+B}\).

The G_{2} 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?**

- OR
- NAND
- AND
- 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 Y_{1} and Y_{2} 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**

- (A + B).\(\bar{B}\)
- (A.B).\(\bar{B}\)
- (A + B).B
- (A.B) + B

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

The output Y’ of the OR gate. G_{1} is Y’ = A + B and the output of G_{2} is \(\bar{B}\). G_{3} is an AND gate whose output is

**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.**

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

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

The symbols given in the question are for the

- OR,
- AND,
- NOT and
- NAND gates

**Question 6. The circuit given here is equivalent to**

- An AND gate
- A NAND gate
- A NOR gate
- A OR gate

**Answer:** 3. A NOR gate

The output of the (NOR gate) G_{1} is \(Y^{\prime}=\overline{A+B}\)

The output of the (NAND gate) G_{2} is Y” = \(Y^{\prime \prime}=\overline{Y^{\prime}}=\overline{A+B}=A+B\)

The output of the (NOT gate) G_{3} 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**

- A = 1, B = 0, C = 0
- A = 1, B = 1, C = 0
- A = 1, B = 0, C = 1
- A = 0, B = 1, C = 0

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

The output of G_{1} (an OR gate) is Y’ = A + B.

The output Y of G_{2} (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?**

- 0 and 1
- 0 and 0
- 1 and 0
- 1 and 1

**Answer:** 3. 1 and 0

The output of the AND gate G_{1} is Y’ = A.B

The output of the NAND gate G_{2} 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**

- \(Y=\bar{A} \cdot \bar{B}\)
- \(Y=\overline{A \cdot B}\)
- Y = A.B
- Y = \(Y=\overline{A+B}\)

**Answer:** 3. Y = A.B

In the given circuit, G_{1} is a NAND gate and G_{2} 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, G_{1} represents a NOR gate and G_{2} is effectively NOT gate.

The output of G_{1} 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**

- OR gate
- AND gate
- XOR gate
- 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
- 2
- 3
- 4

**Answer:** 2. 2

- Is a NAND gate with the output Y = \(\overline{1 \cdot 1}=\overline{1}\) = 0.
- Is a NAND gate with the output Y = \(\overline{0 \cdot 1}=\overline{0}\) = 1.
- Is a NOR gate with the output Y = \(\overline{1+1}=\overline{1}\) = 0.
- 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**

- NOR gate
- AND gate
- OR gate
- 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**

- A NOR gate
- An OR gate
- A NAND gate
- 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**

- AND gate
- NAND gate
- OR gate
- 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**

- AND
- OR
- NAND
- 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 Y_{1} be the output of the given OR gate. With Y_{1} 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**

- X = 0 and Y = 0
- X = 1 and Y = 0
- X = 1 and Y = 1
- 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**

- \(A \cdot \bar{B}\)
- \(\bar{A} \cdot B\)
- A.B + \(\overline{A \cdot B}\)
- \(A \cdot \bar{B}+\bar{A} \cdot B\)

**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**

- AND gate
- NOR gate
- NANDgate
- 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**

- AND gate
- OR gate
- NOR gate
- 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.