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

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.

The correct answer is option 3: NOT gate

Key Points

• A NAND gate gives output 0 only when both inputs are 1; otherwise, the output is 1.
• The Boolean expression for NAND is:
• If both inputs are connected together, say input A = B, then:
• This is equivalent to the operation of a NOT gate.

Additional Information

• OR Gate: Performs logical addition (A + B)
• AND Gate: Performs logical multiplication (A ⋅ B)
• EX-OR Gate: Outputs 1 only when inputs differ (A ⊕ B)
• NOT Gate: Outputs the complement of the input, which is what a NAND gate behaves like when both inputs are same

Hence, the correct answer is: option 3: NOT gate

Concept:

The given Boolean function is .

We are to implement this function using only 2-input NAND gates and assuming only normal (i.e., uncomplemented) inputs are available.

Step-by-step NAND Implementation:

1. Generate B’:
Using NAND gate: → 1 gate

2. Generate AB’:
Use NAND to AND: → 2 gates

3. Generate BC:
→ 2 gates

4. Generate AC:
→ 2 gates

5. ORing all three terms:
To implement , we use NAND-based OR with DeMorgan’s law:
→ Requires 2 NANDs for each OR combination.
Three terms OR can be done in 3 NAND gates optimally.

Total NAND Gates Required:

• 1 (B’)
• 2 (AB’)
• 2 (BC)
• 2 (AC)
• 3 (Final OR)

Total = 1 + 2 + 2 + 2 + 3 = 10 gates

Optimization:

With gate sharing and smart logic restructuring, it is possible to reduce the count. The minimum number of 2-input NAND gates required after such optimization is 4.

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:

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:

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: