Combinational Circuits MCQ Quiz - Objective Question with Answer for Combinational Circuits - Download Free PDF

A half adder circuit is made up of an AND gate with an XOR gate as shown below:

• A half adder is also known as XOR gate because XOR is applied to both inputs to produce the sum
• Half adder can add only two bits (A and B) and has nothing to do with the carry
• If the input to a half adder has a carry, then it will neglect it and adds only the A and B bits
• That means the binary addition process is not complete and that's why it is called a half adder

Sum (S) = A⊕B, Carry = A.B

The correct answer is: The encoder will output the binary code for the highest priority active input.

Explanation:

A priority encoder is a combinational circuit that:

• Accepts multiple input lines, but only one output is generated at a time.

• If two or more inputs are active simultaneously, the input with the highest priority (usually the one with the highest input number) is encoded and reflected at the output.

This ensures unambiguous output even when multiple inputs are high.

🔍 Example:

For a 4-to-2 priority encoder with inputs D3 to D0 (D3 has highest priority):

Explanation:

Error Detector (Comparator)

Definition: An error detector, commonly referred to as a comparator, is an electronic device or circuit that compares two input signals and determines the difference between them. It is widely used in control systems, instrumentation, and signal processing to ensure the desired performance and identify deviations or errors. The comparator plays a crucial role in maintaining the stability and accuracy of systems by continuously monitoring and correcting errors.

Working Principle:

The comparator operates by comparing an input signal (usually the actual state or condition of a system) with a reference signal (desired state or condition). The difference between these signals is called the error signal. This error signal is then processed to make adjustments to the system, bringing it closer to the desired state.

• Input signals: The comparator receives two inputs – the reference signal and the actual signal.
• Comparison: The comparator compares these inputs and calculates the error signal.
• Output: The error signal is generated, which can be used to trigger corrective actions or adjustments in the system.

Applications:

• Control Systems: Comparators are extensively used in control systems, such as PID controllers, where the error signal is utilized to adjust system parameters and achieve stability and precision.
• Instrumentation: Error detectors are employed in measurement and instrumentation systems to ensure accurate readings by identifying discrepancies between actual and expected values.
• Signal Processing: Comparators are used in circuits for signal processing, such as in analog-to-digital converters, oscillators, and pulse width modulation (PWM) circuits.

Advantages:

• Provides high precision in detecting errors.
• Enables corrective measures to maintain system stability and accuracy.
• Simple and cost-effective design for many applications.

Disadvantages:

• May require additional components for complex systems to process the error signal effectively.
• Limited functionality in systems with highly nonlinear behavior.

Correct Option Analysis:

The correct option is:

Option 3: Comparator

In the context of error detection, a comparator functions as an error detector by comparing two signals – the actual state of the system and the desired state – and generating an error signal. This error signal helps in identifying deviations and initiating corrective actions. Comparators are fundamental components in control systems, ensuring the system operates as intended.

Additional Information

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

Option 1: Multiplexer

A multiplexer is a device used to select one input signal from multiple input signals and forward it to a single output line. It does not perform error detection or comparison between signals. Instead, its primary function is to manage multiple data streams and direct them appropriately, which is unrelated to the functionality of error detectors.

Option 2: Decoder

A decoder is a device that translates encoded data into its original format. For example, in digital systems, it converts binary codes into human-readable formats or specific outputs. While decoders play a crucial role in communication and data processing systems, they do not perform error detection or signal comparison, which is the primary function of an error detector.

Option 4: Integrator

An integrator is a circuit that performs mathematical integration on an input signal, producing an output that represents the cumulative sum of the input signal over time. Integrators are commonly used in signal processing and control systems for tasks like smoothing signals or calculating areas under curves. However, they do not serve as error detectors or comparators.

Conclusion:

An error detector, or comparator, is an essential component in electronic systems, particularly in control and instrumentation applications. Its ability to compare signals and generate an error signal enables accurate monitoring and corrective actions to maintain system stability and performance. While other devices like multiplexers, decoders, and integrators serve important roles in electronic systems, they do not perform the function of error detection. Therefore, the correct option for this question is Option 3: Comparator.

Explanation:

3-bit Gray Counter Controlled Multiplexer

Definition: A 3-bit Gray counter is a type of binary counter in which two successive values differ in only one bit. This counter is used to control the output of a multiplexer, which selects one of several input signals and forwards the selected input to a single output line.

Working Principle: In the given scenario, the 3-bit Gray counter is used to control the multiplexer’s output. The counter starts from an initial state of 000 and goes through a sequence of states where only one bit changes at a time. The output of the multiplexer is pulled high when it is not enabled.

The Gray code sequence for a 3-bit counter is as follows:

• 000
• 001
• 011
• 010
• 110
• 111
• 101
• 100

Sequence Analysis:

With the initial state of the counter being 000, the multiplexer will follow the Gray code sequence mentioned above. The multiplexer is enabled only for certain states, and the output is high (1) when it is not enabled. Let’s analyze the sequence step-by-step:

1. 000: Multiplexer selects I0.
2. 001: Multiplexer is not enabled, output is 1.
3. 011: Multiplexer is not enabled, output is 1.
4. 010: Multiplexer selects I1.
5. 110: Multiplexer selects I3.
6. 111: Multiplexer is not enabled, output is 1.
7. 101: Multiplexer is not enabled, output is 1.
8. 100: Multiplexer selects I2.

Based on this analysis, the output sequence of the circuit is:

I0, 1, 1, I1, I3, 1, 1, I2

Correct Option Analysis:

The correct option is:

Option 1: I0, 1, 1, I1, I3, 1, 1, I2

This option correctly describes the output sequence of the multiplexer controlled by the 3-bit Gray counter

The correct answer is a type of circuit.
Key Points

• A logic gate is a fundamental building block of digital circuits.
• It performs a basic logical function, such as AND, OR, NOT, NAND, NOR, XOR, and XNOR.
• Logic gates process one or more input signals to produce an output signal based on a certain logic.
• They are used in various electronic devices to perform computations and make decisions.
• Logic gates are implemented using diodes, transistors, and other electronic components.

Additional Information

• AND Gate
  • An AND gate outputs true (1) only if all its inputs are true (1).
  • It performs a logical conjunction operation.
• OR Gate
  • An OR gate outputs true (1) if at least one of its inputs is true (1).
  • It performs a logical disjunction operation.
• NOT Gate
  • A NOT gate outputs the inverse of its input.
  • If the input is true (1), the output is false (0), and vice versa.

Decoder:

The decoder is a combinational ckt, that convert Binary Coded information into Familiar, representation like the decimal, octal, Hexadecimal, etc.

The decoder has ‘n’ no of i/p & less than equal to 2n O/P

i.e., \(\begin{array}{*{20}{c}} {n \le }&{{2^n}}\\ {\frac{I}{P}}&{\frac{O}{P}} \end{array}\)

For 4 input lines n = 4

Maximum output lines = 2⁴ = 16

Additional Information

Multiplexer (MUX) is defined as:

Based on the select line, it selects the input & produces its output. i.e., at a time one input is taken to get output.

“MUX” is also known as

→ Data selector

→ Parallel to serial converter

→ Many to one circuit.

→ Universal logic Ckt.

Combinational Logic circuits are circuits for which the present output depends only on the present input, i.e. there is no memory element to store the past output.

A combinational circuit can have ‘n’ number of inputs and ‘m’ number of outputs as shown:

Combinational circuits are:

• Multiplexer/Demultiplexer
• Encoder/Decoder
• Adders
• Subtractors
• Code Converters

Multiplexers:

• A multiplexer is Many to one data selector.
• A multiplexer selects one of the many data available at its input depending on the bits on the select line.
• For 2m inputs, there are m select lines that determine which input is to be connected to the output.

In a sequential circuit, the output depends on both the present and the past values. The circuit diagram is as shown:

Examples of sequential circuits:

• Shift Registers
• Flip flops
• Counters

Concept:

In a 4 × 1 MUX

Truth-Table

Y = Output = S̅₁ S̅₀ I₀ + S̅₁ S₀ I₁ + S₁ S̅₀ I₂ + S₁ S₀ I₃

MUX contains AND gate followed by OR gate

Calculation:

By re-drawing circuit diagram

∴ I₀ = 0, I₁ = 1, I₂ = 1, I₃ = 0 & (P = S₁, Q = S₀)

Now output of 4 × 1 MUX is

Y = F = (P̅ Q̅) 0 + (P̅ Q)1 + (P Q̅) 1 + (P Q)0

∴ F = P Q̅ + P̅ Q = P ⊕ Q

∴ F = XOR (P, Q) 

The correct option is 1

Concept:

Multiplexer: It is a device that combines several inputs and outputs them into a single line.

Demultiplexer: It is a device that reverses the process of multiplexer i.e. it converts data from a single input line to multiple output lines.

NAND Gate:

• NAND gate represents the complement of the AND operation.
• The graphic symbol for the NAND gate consists of an AND symbol with a bubble on the output, denoting that a complement operation is performed on the output of the AND gate. 
• The logic NAND function can be expressed by the Boolean expression of, A.B.

​

Analysis:

Given A = 1100 and B = 1010

∴ The output will be 0111.

Half adder circuit have two inputs and two outputs (sum and carry).

A half adder circuit is made up of an AND gate with an XOR gate as shown below:

• A half adder is also known as XOR gate because XOR is applied to both inputs to produce the sum
• Half adder can add only two bits (A and B) and has nothing to do with the carry
• If the input to a half adder has a carry, then it will neglect it and adds only the A and B bits
• That means the binary addition process is not complete and that's why it is called a half adder

Sum (S) = A⊕B, Carry = A.B

Combinational Logic circuits are circuits for which the present output depends only on the present input, i.e. there is no memory element to store the past output.

A combinational circuit can have ‘n’ number of inputs and ‘m’ number of outputs as shown:

Combinational circuits are:

• Multiplexer/Demultiplexer
• Encoder/Decoder
• Adders
• Subtractors
• Code Converters

In a sequential circuit, the output depends on both the present and the past values. The circuit diagram is as shown:

Examples of sequential circuits:

• Shift Registers
• Flip flops
• Counters

Concept:

The output of a NOR gate will be at logic 1 when all the input is at logic 0.

• NOR gate is the output (f).
• For the NOR gate whenever there is input(high), It gives Zero.
• The NOR gate is connected with \(D_1,D_4 and D_7\) only, so we have to look after those input only.

Hence, the output of the given circuit is given as:

F = ∑m (0, 2, 3, 5, 6)

Concept: 

For a 2 × 1 MUX is shown above, the output function F is expressed as:

F = S̅₁ I₀ + S₁I₁

i.e. when S₁ = 0, I₀ is transmitted to the output.

And when S₁ = 1, I₁ is transmitted to the output.

Analysis:

The given circuit is redrawn as:

F₁ = S̅₁ w + S₁ w̅

F₁ = S₁ ⊕ w

Now, the required function f will be:

F₂ = F = S̅₂F₁ + S₂F̅₁

F = S₂ ⊕ F₁

F = S₂ ⊕ S₁ ⊕ w

Encoder:

• It is a combinational circuit which converts decimal number into binary number.
• It consists 2ⁿ input lines and n output lines.
• They do not have any select lines.

Additional Information

Decoder:

• It is a combinational circuit which converts binary number into decimal number.
• It consists n input lines and 2ⁿ output lines.
• They also do not have any select lines.

Multiplexer:

• It is a combinational circuit which have many data inputs and single output depending on control or select inputs.​
• For 2^m input lines , m selection lines are required in multiplexer.

De-Multiplexer:

• It is a combinational circuit which have single data input and many data output depending on control or select inputs.​
• For 2^m output lines, m selection lines are required in de-multiplexer.