Logic Gates MCQ Quiz - Objective Question with Answer for Logic Gates - Download Free PDF

Concept:

The given Boolean expression is:

It was to be realized using AND and OR gates. But all 2-input AND gates were mistakenly replaced by 2-input NAND gates.

We need to determine the new expression with these incorrect gates.

Step-by-Step Evaluation:

Let’s denote the original terms:

T1 =

T2 =

T3 =

Now, replacing each **AND** with **NAND**, each term becomes:

— since second AND also becomes NAND

Similarly for other terms:

and

Each term is now a NAND of a NAND and a variable → effectively behaves like NOR logic and outputs tend to 1 for all combinations.

Let’s test values for all combinations of a, b, c (truth table) — we find that output is 1 for all cases due to the nature of NAND-ing every AND gate. The circuit effectively turns into one that always outputs logic high (1).

Explanation:

The Circuit Behaves as a NOR Gate

Definition of a NOR Gate: A NOR gate is a digital logic gate that performs the logical NOR operation. It is a combination of an OR gate followed by a NOT gate. In Boolean algebra, the NOR operation is expressed as Y = ¬(A + B), where Y is the output, and A and B are the inputs. The NOR gate outputs a HIGH (1) only when all its inputs are LOW (0); otherwise, it outputs LOW (0).

Truth Table for a 2-Input NOR Gate:

Working Principle of the NOR Gate:

• The inputs of the NOR gate are combined using an OR gate, which performs the logical OR operation (A + B).
• The output of the OR gate is then inverted (NOT operation) to produce the final NOR output.
• As a result, the NOR gate outputs HIGH (1) only when both inputs are LOW (0). For any other combination of inputs, the output is LOW (0).

Applications of NOR Gates:

• Basic Building Block: NOR gates are considered universal gates and can be used to implement any other logic gate, such as AND, OR, and NOT.
• Control Systems: Used in digital control systems where specific conditions need to be satisfied to activate a process or operation.
• Memory Circuits: Often used in the construction of flip-flops and other storage elements in digital memory circuits.

Advantages of NOR Gates:

• Simple and versatile, making them a fundamental component in digital electronics.
• Can be used to construct any other logic gate, reducing the need for multiple gate types in a circuit design.

Correct Option Analysis:

The correct option is:

Option 3: NOR Gate

This option is correct because the circuit described exhibits the characteristics of a NOR gate. The truth table and logical operation of the circuit align with the NOR gate's definition, where the output is HIGH only when all inputs are LOW. The NOR gate is an essential component in digital electronics and serves as a universal gate due to its ability to perform the functions of all other basic gates.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: AND Gate

An AND gate performs the logical AND operation, where the output is HIGH (1) only when all inputs are HIGH (1). Its Boolean expression is Y = A × B. This option is incorrect because the circuit does not exhibit the characteristics of an AND gate. For example, when both inputs are LOW (0), the AND gate would output LOW (0), but the described circuit outputs HIGH (1), which is inconsistent with AND gate behavior.

Option 2: OR Gate

An OR gate performs the logical OR operation, where the output is HIGH (1) if any of the inputs are HIGH (1). Its Boolean expression is Y = A + B. This option is incorrect because the circuit outputs HIGH (1) only when both inputs are LOW (0), which is the opposite of an OR gate's behavior. The circuit includes a NOT operation that inverts the OR gate's output, making it a NOR gate instead.

Option 4: NAND Gate

A NAND gate performs the logical NAND operation, which is the inverse of the AND operation. Its Boolean expression is Y = ¬(A × B). The NAND gate outputs HIGH (1) unless all inputs are HIGH (1). This option is incorrect because the circuit described does not perform the NAND operation. The truth table and logical expression do not match those of a NAND gate.

Option 5: Not Provided

This option is invalid as it does not describe any logic gate or operation. It cannot be considered as a correct representation of the circuit's behavior.

Conclusion:

By analyzing the given circuit's behavior, it is evident that it functions as a NOR gate. The circuit's logical operation, truth table, and output characteristics match those of a NOR gate. Furthermore, the incorrect options represent other logic gates or invalid descriptions that do not align with the circuit's operation. The NOR gate's versatility and importance in digital electronics make it a fundamental component in designing and implementing logic circuits.

The correct option is 4

Concept:

From the truth table, it is clear that the output of an EX-OR gate is '0' when both inputs are '1'. This is because the EX-OR gate outputs '1' only when the inputs are different. When both inputs are the same (either both 0 or both 1), the output is '0'. Therefore, the correct answer is option 4.

The primary goal of simplifying a Boolean expression before implementing it with gates is: 3) To reduce the number of gates and interconnections

Explanation:

• Minimizing gates reduces the circuit's cost, complexity, and physical space required.
• Fewer interconnections improve reliability (less chance of wiring errors or signal interference).
• Optimized circuits consume less power and operate faster (fewer propagation delays).

Explanation:

Universal Gate

Definition: A universal gate is a type of logic gate that can be used to implement any Boolean function without needing to use any other type of gate. Universal gates are versatile and are fundamental in digital electronics because they can be used to construct other basic gates such as AND, OR, and NOT gates.

Correct Option: The correct answer is Option 3: NOR Gate.

Explanation:

The NOR gate is called a universal gate because it can be used to create all the other basic logic gates (AND, OR, NOT, NAND, and XOR). The NOR gate is a combination of the OR gate followed by a NOT gate. It outputs a logical "1" only when all inputs are logical "0". The truth table for a NOR gate is as follows:

Why NOR Gate is Universal:

• Implementation of NOT Gate: A single input NOR gate acts as a NOT gate. If the input is "A", the output will be "NOT A".
• Implementation of OR Gate: By combining two NOR gates, an OR gate can be constructed.
• Implementation of AND Gate: By using multiple NOR gates in a specific configuration, an AND gate can be created.
• Implementation of XOR Gate: XOR gates can also be constructed using NOR gates, but it requires a more complex arrangement.

Because of its ability to replicate all other logic gates, the NOR gate is classified as a universal gate. This feature is extremely useful in digital circuit design, as it allows for simplification and standardization in hardware implementations.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: AND Gate

The AND gate is a basic logic gate that outputs "1" only when all its inputs are "1". It is not a universal gate because it cannot be used to construct other gates by itself. While it is a fundamental gate in digital circuits, it lacks the versatility of universal gates like NOR and NAND.

Option 2: NOT Gate

The NOT gate is a unary operator that outputs the inverse of its input. While it is essential for negation in digital logic, it is not a universal gate. It cannot construct other gates without additional components.

Option 4: EX-OR Gate

The XOR gate outputs "1" when its inputs are different. Although it has unique properties and is widely used in applications like parity checking and error detection, it is not a universal gate. It cannot be used to construct other gates independently.

Option 5: NAND Gate

Although not listed as the correct answer in the question, the NAND gate is also a universal gate. Like the NOR gate, it can be used to construct all other basic logic gates, making it equally versatile. If the question had included NAND gate as an option, it would also have been correct.

Conclusion:

The NOR gate is a universal gate because it can be used to implement any Boolean function and construct all other basic logic gates. This versatility makes it essential in digital electronics and circuit design. While other gates like AND, NOT, and XOR serve specific purposes, they lack the ability to replicate all other gate functions, which is the defining characteristic of universal gates. Alongside NOR gates, NAND gates also share the universal gate classification.

Concept:

XNOR Gate:

Symbol:

​

Truth Table:

Output Equation: 

1) If B is always Low, the output is the inverted value of the other input A, i.e. A̅.

2) The output is low when both the inputs are different.

3) The output is high when both the inputs are the same.

4) XNOR gate produces an output only when the two inputs are same.

Analysis:

The number of 2-input NAND gates required to implement a 2-input XOR gate is 4.

Similarly, the number of 2-input NOR gates required to implement a 2-input XNOR gate is 4.

XOR GATE

Symbol:

Truth Table:

Output Equation: 

Key Points: 

1) If B is always High, the output is the inverted value of the other input A, i.e. A̅.

1) The output is low when both the inputs are the same. 

2) The output is high when both the inputs are different.

Explanation:

Y = 1

Output expression Q is equivalent to NAND gate.

Important Points

NAND GATE

Symbol:

Truth Table:

Output Equation: 

Key Points:

1) If A is always High, the output is the inverted value of the other input B, i.e. B̅

2) The output is low only when both the inputs are high

3) It is a universal gate

Concept:

Propagation Delay:

The propagation delay, or gate delay, is the length of time that starts when the input to a logic gate becomes stable and valid to change, to the time that the output of that logic gate is stable and valid to change.

T = 2n Tpd

Here 2 is multiplied with the propagation delay when logic gates are connected in feedback.

T is the time period of the output

n is the number of logic gates

Tpd is the propagation delay of one gate

Calculation:

Given, 

n = 3 as there are three gates with feedback

Tpd = 100 nsec

T = 2 × 3 × 10^-7

T= 6 × 10-7

Fundamental Frequency is given by f

f = 1.67 × 10⁶

f = 1.67 MHz

Concept:

In Digital Electronics, Logic 1 means High and Logic 0 means low.

Whenever in diode, if 1 is applied to anode and 0 to cathode then Diode acts as a short circuit i.e. ON.

And if 0 is applied to anode and 1 to cathode Diode acts as open circuit i.e. OFF.

Explanation:

The given logic circuit is

For different logic of A and B,4 cases are there and according to that logic of C will vary.

Case 1

When A is logic 0 and B is logic 0

Then the logic of C will be 0.

Case 2

When A is logic 0 and B is logic 1

Then the logic of C will be 1.

Case 3

When A is logic 1 and B is logic 0

Then the logic of C will be 1.

Case 4

When A is logic 1 and B is logic 1

Then the logic of C will be 1.

According to Result, we make a table

This Table is of Logic OR gate.

∴ C = A + B

Important Points

Logic Circuit for AND gate is C = AB

The given gate is an XNOR gate. NOR gate is an OR gate followed by a NOT gate.

Symbol:

Truth Table:

Output Equation: 

Key Points: 

1) If B is always Low, the output is the inverted value of the other input A, i.e. A̅.

1) The output is low when both the inputs are different.

2) The output is high when both the inputs are the same.

The figure below shows the IEEE/ANSI symbols alongside the traditional symbols for the basic gates:

Logic gates:

• A logic gate is an idealized or physical electronic device implementing a Boolean function.

• A logical operation performed on one or more binary inputs that produce a single binary output.

If A and B are given as input then:

Concept:

3 variable K-maps:

• For a 3-variable Boolean function, there is a possibility of 8 output minterms.
• The general representation of all the minterms using 3-variables is shown below.

Calculation:

Given Boolean expression is,

F = AB + AC̅ + BC

= A B C̅ + A B C + A B̅ C̅ + A B C̅ + A B C + A̅ B C

F = BC + AC̅

NOR gate:

• It is a digital circuit having two or more inputs but only one output.
• It gives a high output if either input A or B or both are low (0) otherwise it gives a high output (1).
• It is described by the Boolean expression: 
• The above logic gate is the NOR gate.

The truth table for NOR gate: