All questions of Combinational Circuits for Computer Science Engineering (CSE) Exam

Explanation:
A full adder is a combinational circuit that is used to perform addition of two binary numbers along with a carry input. It takes three inputs - two bits to be added (A and B) and a carry input (Cin). The output of a full adder consists of two bits - Sum (S) and Carry-out (Cout).

A 3-bit full adder is a circuit that can perform addition of three 3-bit numbers. It takes three sets of inputs - A0, B0, Cin for the least significant bit, A1, B1, Cin for the middle bit, and A2, B2, Cin for the most significant bit.

Inputs:
A 3-bit full adder has a total of 9 inputs: 3 inputs for each bit.

- A0, A1, A2 are the inputs for the first number's bits.
- B0, B1, B2 are the inputs for the second number's bits.
- Cin is the carry input.

Outputs:
A 3-bit full adder produces three sets of outputs: Sum (S0, S1, S2) and Carry-out (Cout).

- S0, S1, S2 are the outputs for the sum of the corresponding bits.
- Cout is the carry-out from the most significant bit.

Combination:
The number of combinational inputs is the sum of the number of inputs required for each bit. In this case, there are 3 bits, so the total number of combinational inputs is:

3 (inputs for A) + 3 (inputs for B) + 1 (carry input) = 7

However, we need to include the carry-out from the previous bit as well. Since there are 3 bits, we need to consider the carry-out from the second bit for the third bit's addition. Therefore, the total number of combinational inputs is:

7 (inputs for A, B, and Cin) + 1 (carry-out from the previous bit) = 8

Hence, the correct answer is option D) 8 combinational inputs.

A multiplexer, also known as a mux, is a device used in digital circuits to combine multiple input signals into a single output signal. It is commonly used in communication systems, digital data processing, and various other applications. The correct answer to the question is option 'B', which states that a multiplexer is a device that converts many signals into one.

Here is a detailed explanation of why option 'B' is the correct answer:

What is a multiplexer?
A multiplexer is a digital circuit that selects one of many input signals and forwards it to a single output line. It is often represented with the symbol "MUX". The selection of the input signal is controlled by a set of control signals, known as select lines.

Working Principle
The working principle of a multiplexer is based on the concept of digital switching. It has multiple input lines, one output line, and select lines. The number of input lines depends on the configuration of the multiplexer. For example, a 4-input multiplexer will have four input lines.

Functionality
The multiplexer works by using the select lines to enable one of the input lines and ignore the others. The selected input signal is then passed through to the output line. The selection process is based on the binary value of the control signals. Each control signal combination corresponds to a specific input line.

Advantages and Applications
- Multiplexers are used in communication systems to combine multiple data streams into one transmission line, thus increasing the efficiency of data transmission.
- They are used in digital data processing to select data from multiple sources and route it to the desired destination.
- Multiplexers can also be used for data storage and retrieval, as they allow multiple inputs to share a single output line.

In conclusion, a multiplexer is a device that combines multiple signals into one output signal. It is widely used in various digital applications and plays a crucial role in improving the efficiency of data transmission and processing.

The number 2 is an integer and does not have a numerical value.

DTMF (Dual Tone Multiple Frequency)
DTMF stands for Dual Tone Multiple Frequency. It is a signaling system used for telephone signaling over analog telephone lines in the voice-frequency band between telephone handsets and other communications devices and switching centers.

How DTMF works
- DTMF assigns a specific frequency (consisting of two separate tones) to each key on the phone keypad.
- When a key is pressed on the phone, it generates a combination of these two frequencies.
- The tones are decoded at the receiving end to determine which key was pressed.

Usage of DTMF
- DTMF is commonly used for interactive voice response systems, in which a user navigates through a menu by pressing keys on their phone.
- It is also used in telephone banking, credit card transactions, and various other automated systems.

Advantages of DTMF
- DTMF is more reliable than pulse dialing systems as it is less prone to errors.
- It allows for faster and more accurate transmission of signals over telephone lines.

Conclusion
In conclusion, DTMF is a widely used signaling system that plays a crucial role in enabling communication and interaction with automated systems over telephone networks. Its reliability, speed, and accuracy make it a preferred choice for various applications in telecommunication.

To answer this question, we need to understand how a decoder works and how many output lines it will have based on the number of input lines.

A decoder is a combinational logic circuit that converts an input code into an output code. It is commonly used to decode binary information and is often used in digital systems, such as computers.

A decoder with 4 input lines will have 2^4 = 16 possible input combinations. Each input combination will correspond to a unique output line in the decoder.

Now, let's go through each option and determine the number of output lines:

a) 15: This option is incorrect because a decoder with 4 input lines will have 16 output lines, not 15.

b) 16: This option is correct. As mentioned earlier, a decoder with 4 input lines will have 16 output lines.

c) 17: This option is incorrect because a decoder with 4 input lines will not have 17 output lines.

d) 18: This option is incorrect because a decoder with 4 input lines will not have 18 output lines.

Therefore, the correct answer is option 'B', which represents 16 output lines for a decoder with 4 input lines.

In summary, the number of output lines for a decoder with 4 input lines is 16.

Explanation:

To decode binary 1101, we need to determine the combination of logic gates that can produce the output based on the input.

Binary 1101:
The binary number 1101 represents the decimal number 13. In order to decode this binary number, we need to determine the logic gates that can produce an output of 13 based on the input.

Options:
Let's evaluate each option to determine which one can decode binary 1101.

Option a) One 4-input AND gate:
An AND gate produces a high output only when all of its inputs are high. Since we have only one 4-input AND gate, it cannot produce the desired output of 13. Therefore, option a is incorrect.

Option b) One 4-input AND gate, one inverter:
An inverter, also known as a NOT gate, produces the opposite logic level of its input. By using a 4-input AND gate and an inverter, we can create a combination that produces the desired output of 13.

Explanation:
- The 4-input AND gate takes four inputs and produces a high output only when all four inputs are high.
- By connecting the binary inputs to the AND gate, we can ensure that the output will be high only when the binary input is 1101.
- However, the output of the AND gate will be the opposite of what we desire (low instead of high).
- By connecting the output of the AND gate to an inverter, we can invert the logic level and obtain the desired output of high when the input is 1101.

Conclusion:
Option b, which includes a 4-input AND gate and an inverter, is the correct combination of logic gates that can decode binary 1101.

Invalid BCD to Valid BCD Conversion

Invalid BCD can be made valid by adding with 0110 (option B).

1. BCD Representation
BCD (Binary Coded Decimal) is a numeric representation where each decimal digit is represented by a 4-bit binary code. The valid BCD digits range from 0000 to 1001, representing the decimal values 0 to 9.

2. Invalid BCD
Invalid BCD refers to a BCD representation that violates the rules of BCD. In BCD, each digit must be in the range of 0000 to 1001. If a digit exceeds this range, it is considered invalid.

3. Adding with 0110
To convert an invalid BCD to a valid BCD, we can add a valid BCD digit to the invalid digit. In this case, adding with 0110 (option B) will make the BCD valid.

4. Explanation
The BCD digits 0000 to 1001 represent the decimal values 0 to 9. Adding any of these valid BCD digits to an invalid BCD digit will bring it back within the valid range.

For example, let's say we have an invalid BCD digit "1011". Adding it with 0110 (option B) gives us:

1 0 1 1 (invalid BCD)
+ 0 1 1 0 (0110)
-----------
1 0 0 0 1 (valid BCD)

The result "10001" is a valid BCD digit representing the decimal value 1.

5. Conclusion
In conclusion, to convert an invalid BCD to a valid BCD, we can add a valid BCD digit to the invalid digit. Adding with 0110 (option B) will ensure that the BCD becomes valid.

Understanding the Problem
To construct a 6 × 64 line decoder, we need to decode 6 input bits into 64 output lines. A 3 × 8 line decoder can decode 3 input bits into 8 output lines.
Breaking Down the Requirements
- Inputs: The 6 input lines can be divided into two groups.
- First Group: Utilize 3 bits for the first decoder.
- Second Group: Utilize 3 bits for the second decoder.
Using 3 × 8 Line Decoders
1. First Level Decoding:
- Use 1 decoder for the first 3 input bits.
- This decoder will provide 8 outputs, each corresponding to a unique combination of the first 3 bits.
2. Second Level Decoding:
- Each output of the first decoder can enable one of the 8 second decoders.
- Each of these second decoders will take the remaining 3 bits as input.
- Since there are 8 outputs from the first decoder, we need 8 second decoders.
Total Count of Decoders
- 1 decoder for the first level.
- 8 decoders for the second level.
Final Calculation
By summing the decoders:
- Total decoders = 1 (first level) + 8 (second level) = 9 decoders needed.
Thus, the correct answer is option C: 9.
This arrangement allows decoding of all 6 bits into 64 unique outputs using only 3 × 8 line decoders.

1-to-8 Multiplexer

A multiplexer is a combinational circuit that selects one of many inputs and directs it to a single output based on the control signals. In a 1-to-8 multiplexer, there are 8 data inputs, one output, and 3 control input lines.

Working of a 1-to-8 Multiplexer

A 1-to-8 multiplexer has 8 data inputs, labeled D0 to D7, and 3 control input lines, labeled A, B, and C. The control input lines determine which data input is selected and passed to the output.

The control input lines can represent 3 binary values: 000, 001, 010, 011, 100, 101, 110, and 111. These binary values can be used to select one of the 8 data inputs.

Implementation of a 1-to-8 Multiplexer using AND gates

To implement a 1-to-8 multiplexer using AND gates, we need to consider the truth table of the multiplexer and derive the logic expressions for the output based on the control input.

The truth table for a 1-to-8 multiplexer is as follows:

| A | B | C | D0 | D1 | D2 | D3 | D4 | D5 | D6 | D7 | Y |
|---|---|---|----|----|----|----|----|----|----|----|---|
| 0 | 0 | 0 | X | X | X | X | X | X | X | X | Y |
| 0 | 0 | 1 | X | X | X | X | X | X | X | X | Y |
| 0 | 1 | 0 | X | X | X | X | X | X | X | X | Y |
| 0 | 1 | 1 | X | X | X | X | X | X | X | X | Y |
| 1 | 0 | 0 | X | X | X | X | X | X | X | X | Y |
| 1 | 0 | 1 | X | X | X | X | X | X | X | X | Y |
| 1 | 1 | 0 | X | X | X | X | X | X | X | X | Y |
| 1 | 1 | 1 | X | X | X | X | X | X | X | X | Y |

From the truth table, we can derive the logic expressions for the output Y as follows:

Y = (A' * B' * C' * D0) + (A' * B' * C * D1) + (A' * B * C' * D2) + (A' * B * C * D3) + (A * B' * C' * D4) + (A * B' * C * D5) +

Explanation:

To understand why the correct answer is option 'B', let's break down the question and analyze the given information step by step.

Given:
- The number of selected input lines is denoted by 'n'.
- The number of selected input lines, n, is equal to 2^m.

To Find:
- The number of select lines required.

Analysis:
- The number of selected input lines, n, is given as 2^m. This means that for every value of 'm', the number of selected input lines will be a power of 2.
- Let's consider a few examples to understand this better:
- When m = 0, 2^m = 2^0 = 1. So, in this case, 'n' will be equal to 1.
- When m = 1, 2^m = 2^1 = 2. So, in this case, 'n' will be equal to 2.
- When m = 2, 2^m = 2^2 = 4. So, in this case, 'n' will be equal to 4.
- When m = 3, 2^m = 2^3 = 8. So, in this case, 'n' will be equal to 8.
- From these examples, we can observe that the value of 'n' is always a power of 2.

Explanation:
- The number of select lines required is equal to the number of selected input lines, which is denoted by 'n'.
- From the analysis, we know that 'n' is always a power of 2.
- Therefore, the number of select lines required will be equal to the exponent 'm' in the expression 2^m.
- Hence, the correct answer is option 'B', which represents 'm'.

The Carry Propagation

The carry propagation is an important concept in digital logic circuits, specifically in arithmetic circuits such as adders. It refers to the process of carrying over the carry bit from one bit position to the next during addition or subtraction operations. The carry propagation determines the final result of the operation and ensures that the correct carry bits are generated.

Understanding the Carry Propagation

When performing addition or subtraction in binary, each bit position has two inputs (A and B) and two outputs (Sum and Carry). The carry bit is generated when the sum of two bits at a particular position is greater than or equal to 2. In such cases, a carry bit is generated and propagated to the next bit position.

The Carry Propagation Expression

The carry propagation can be expressed as Cp = A & B, where Cp represents the carry propagation, and A and B are the inputs at a particular bit position. The logical AND operation (&) is used to calculate the carry propagation.

Explanation of Option B

Option B states that the carry propagation can be expressed as Cp = A B. This is the correct answer because it aligns with the expression Cp = A & B mentioned earlier. The symbol represents the logical AND operation in some notations.

Other Options

Option A states that Cp = AB, which is not the correct expression for carry propagation. It does not accurately represent the logical AND operation between A and B.

Options C and D state that all but Y0 are LOW or HIGH, respectively. However, these options do not provide any information about the carry propagation and are not relevant to the given question.

Therefore, the correct answer is option B, Cp = A B, which accurately represents the carry propagation in arithmetic circuits.

Answer:
A combinational logic circuit is a digital circuit that produces an output based solely on the current inputs. It does not have any memory elements or feedback loops.

A multiplexer, also known as a data selector, is a combinational circuit that selects one of many inputs and forwards it to the output line based on the control inputs. It has 2n input lines, where n is the number of control inputs, and a single output line.

Explanation:
Let's analyze the given options and their characteristics:

a) Demultiplexer: A demultiplexer takes a single input line and routes it to one of the 2n output lines based on the control inputs. It has n control inputs and 2n output lines. Therefore, it does not match the given criteria of having 2n input lines.

b) Decoder: A decoder takes n input lines and produces 2n output lines. It activates one of the output lines based on the binary value of the input lines. It does not have 2n input lines and a single output line, so it is not the correct answer.

c) Encoder: An encoder takes 2n input lines and produces n output lines. It encodes the binary value of the input lines into an equivalent value on the output lines. It does not have 2n input lines and a single output line, so it is not the correct answer.

d) Multiplexer: A multiplexer takes 2n input lines and forwards one of them to the output line based on the control inputs. It has n control inputs and a single output line. It matches the given criteria of having 2n input lines and a single output line, so it is the correct answer.

Therefore, the correct answer is option 'D' - Multiplexer.

Building Blocks of Encoders

Encoders are digital electronic devices that are used to convert information from one format to another. They are widely used in digital systems to convert analog signals into digital signals. The basic function of an encoder is to encode the input signals into binary code.

Building blocks of encoders include:

1. NOT gate:
A NOT gate, also known as an inverter, is a basic logic gate that has one input and one output. It produces the logical complement of the input signal. In an encoder, a NOT gate can be used to invert the input signal before it is encoded.

2. OR gate:
An OR gate is a logic gate that takes multiple inputs and produces a logical OR of those inputs at its output. It outputs a high signal if any of the inputs are high. In an encoder, an OR gate can be used to combine multiple input signals and generate a single output signal.

3. AND gate:
An AND gate is a logic gate that takes multiple inputs and produces a logical AND of those inputs at its output. It outputs a high signal only if all of the inputs are high. In an encoder, an AND gate can be used to combine multiple input signals and generate a single output signal.

4. NAND gate:
A NAND gate is a logic gate that is a combination of an AND gate followed by a NOT gate. It takes multiple inputs and produces the logical complement of the logical AND of those inputs at its output. In an encoder, a NAND gate can be used to combine multiple input signals and generate a single output signal.

Correct Answer: Option 'B' (OR gate)

Explanation:
The correct answer is option 'B' because an OR gate is one of the essential building blocks of an encoder. It is used to combine multiple input signals and generate a single output signal. An encoder typically has multiple inputs and a single output, where each input represents a different information bit. The OR gate is used to combine these input signals and generate the encoded output.