All questions of Digital Electronics for Electrical Engineering (EE) Exam

From the simplification , f2=£m(4,7,15)+d(5,6,12,13,14) from the minimization of f2 we get f2=x

Decimal-to-BCD Encoder

The Decimal-to-BCD (Binary-Coded Decimal) encoder is a combinational logic circuit that converts a decimal number to its BCD equivalent. BCD is a binary representation of a decimal number where each decimal digit is represented by a 4-bit binary code.

The BCD code uses four binary bits to represent each decimal digit from 0 to 9. In BCD, the binary codes for 0 to 9 are 0000 to 1001, respectively. For example, the decimal number 7 is represented in BCD as 0111.

To design a Decimal-to-BCD encoder, we need to analyze the input and output requirements.

Input: The input to the Decimal-to-BCD encoder is a 4-bit binary number representing a decimal digit. Since we are converting decimal numbers from 0 to 9, the input can have 10 possible combinations from 0000 to 1001.

Output: The output of the Decimal-to-BCD encoder is a 4-bit BCD code for the input decimal digit. Since each decimal digit is represented by a 4-bit BCD code, the output will also have 4 bits.

Logic Design: To convert a 4-bit binary number to its BCD equivalent, we need to implement a logic circuit that maps each possible input combination to its corresponding BCD output.

- We can use a truth table to determine the required logic for the Decimal-to-BCD encoder.
- The truth table will have 10 rows (for 10 input combinations from 0000 to 1001) and 4 columns (for the 4 output bits of the BCD code).
- By analyzing the truth table, we can determine the logic expressions for each output bit.

Number of OR Gates:

- The Decimal-to-BCD encoder requires 4 output bits, and each output bit can be implemented using an OR gate.
- As the correct answer is option 'D', which states that 4 OR gates are required, it aligns with the requirement of having 4 output bits in the Decimal-to-BCD encoder.

Therefore, the correct answer is option 'D' - 4.

Answer:

To determine the maximum clock frequency that can be used for a 4-bit modulo-6 ripple counter using JK flip-flops, we need to consider the propagation delay of each flip-flop.

Propagation Delay:
Propagation delay is the time it takes for a signal to propagate through a circuit element or system. In this case, the propagation delay refers to the time it takes for the output of a flip-flop to stabilize after a clock edge.

Given that the propagation delay of each flip-flop is 50 ns, we need to ensure that the counter has enough time for all the flip-flops to stabilize before the next clock edge is applied.

Ripple Counter:
A ripple counter is a type of counter circuit where the output of one flip-flop serves as the clock input for the next flip-flop in the sequence. In a 4-bit ripple counter, there are four stages of flip-flops connected in series.

Calculating Maximum Clock Frequency:
To calculate the maximum clock frequency, we need to determine the worst-case scenario where the output of the first flip-flop takes the longest time to propagate through all the flip-flops.

In this case, the worst-case scenario occurs when the initial state of the counter is 1111 (decimal 15). In this state, the next state will be 0000 (decimal 0) after the next clock edge.

The time taken for the counter to transition from 1111 to 0000 is equal to the propagation delay of each flip-flop multiplied by the number of flip-flops in the counter. In this case, it is 50 ns * 4 = 200 ns.

The maximum clock frequency is the reciprocal of the time taken for this transition, i.e., 1 / 200 ns = 5 MHz.

Therefore, the maximum clock frequency that can be used for the 4-bit modulo-6 ripple counter is 5 MHz.

Because minters are called products of logic and of sets of variables

The design of an ALU is based on Combinational logic.


An Arithmetic Logic Unit (ALU) is a fundamental digital circuit that performs arithmetic and logical operations on binary numbers. It is a crucial component of a central processing unit (CPU) in a computer system. The design of an ALU involves various considerations, including its functionality, performance, and implementation.


Combinational logic refers to digital circuits where the output is solely determined by the current input values, without any consideration of previous input values or feedback. In other words, the output is a function of the current input values only and does not depend on any sequence or order of inputs. Combinational logic circuits are designed using logic gates such as AND, OR, NOT, and XOR.


The design of an ALU primarily involves implementing various arithmetic and logical operations using combinational logic circuits. These operations include addition, subtraction, multiplication, division, bitwise operations (AND, OR, XOR), and comparison (greater than, less than, equal to).

Reasons for using Combinational Logic in ALU Design:
- Speed: Combinational logic circuits are faster as they do not require clock signals or sequential elements like flip-flops. ALUs need to perform operations quickly to ensure efficient computation.
- Parallelism: Combinational logic allows multiple operations to be performed simultaneously by processing multiple bits in parallel. This parallelism enhances the speed and efficiency of the ALU.
- Flexibility: Combinational logic circuits can be easily designed and modified to accommodate various arithmetic and logical operations. This flexibility enables the ALU to support a wide range of computational tasks.
- Reduced Complexity: By employing combinational logic, the design of an ALU can be simplified as it eliminates the need for complex sequential elements. This simplification leads to a more efficient and compact ALU design.


In conclusion, the design of an ALU is based on combinational logic. Combinational logic circuits provide speed, parallelism, flexibility, and reduced complexity, making them suitable for implementing arithmetic and logical operations in an ALU.

Physical Size:
- CMOS logic typically has a smaller physical size compared to TTL logic. This is because CMOS technology allows for more components to be packed into a smaller area due to its lower power consumption and smaller transistor size.

Speed of Operation:
- TTL logic generally has a faster speed of operation compared to CMOS logic. This is because TTL uses bipolar transistors which switch faster than CMOS transistors. However, CMOS technology has been continuously improving its speed over the years and in some cases can now match or even surpass TTL speeds.

Power Dissipation:
- CMOS logic has lower power dissipation compared to TTL logic. This is because CMOS transistors consume power only when they switch, whereas TTL transistors draw current continuously. As a result, CMOS logic is more energy efficient and produces less heat.

Conclusion:
- In conclusion, CMOS logic has a smaller physical size and lower power dissipation compared to TTL logic. However, TTL logic may have a slight edge in terms of speed of operation, although CMOS technology has made significant improvements in this area.

Essential Prime Implicant

The correct answer is option 'A', Essential Prime Implicant.

Explanation:
In digital logic design, a prime implicant is a product term that includes all the variables of a Boolean function in its minterm form. In other words, a prime implicant is a minimal expression that covers as many minterms as possible while still being valid.

Implicant:
An implicant is a product term that covers one or more minterms of a Boolean function. It can be a prime implicant or a non-prime implicant.

Complement:
The complement of a Boolean function is the function obtained by interchanging the 1s and 0s in the truth table of the original function.

Prime Complement:
There is no such term as "Prime Complement" in digital logic design.

Essential Prime Implicant:
An essential prime implicant is a prime implicant that covers at least one minterm that is not covered by any other prime implicant. In other words, it is a prime implicant that cannot be eliminated without losing the completeness of the Boolean function.

Importance of Essential Prime Implicants:
- Essential prime implicants are necessary for obtaining a minimal expression of a Boolean function.
- They ensure that all minterms are covered by the expression.
- Without essential prime implicants, the function may not be fully represented and may lead to incorrect results.

Conclusion:
The prime implicant which has at least one element that is not present in any other implicant is known as an Essential Prime Implicant. It is important for obtaining a minimal expression of a Boolean function and ensuring the completeness of the function.

1-to-4 Demultiplexer:
A 1-to-4 demultiplexer is a digital circuit that takes one input signal and selects one of the four output channels based on the control signals. It is the opposite of a multiplexer, which takes multiple input signals and selects one output channel.

Working of a 1-to-4 Demultiplexer:
A 1-to-4 demultiplexer has one input line and four output lines. The number of select lines determines the number of output channels and the corresponding decoder logic. Each select line enables one of the four output channels.

Number of Select Lines:
The number of select lines required in a 1-to-4 demultiplexer can be determined by the formula 2^n, where 'n' is the number of select lines. In this case, we have four output channels (2^2 = 4), so the number of select lines required is '2'.

Explanation:
To understand why the correct answer is option 'A' (2 select lines), let's consider the truth table of a 1-to-4 demultiplexer.

Truth Table:
| S1 | S0 | D0 | D1 | D2 | D3 |
|----|----|----|----|----|----|
| 0 | 0 | I | 0 | 0 | 0 |
| 0 | 1 | 0 | I | 0 | 0 |
| 1 | 0 | 0 | 0 | I | 0 |
| 1 | 1 | 0 | 0 | 0 | I |

In the truth table above, 'S1' and 'S0' are the select lines, 'I' is the input signal, and 'D0', 'D1', 'D2', and 'D3' are the output signals.

Analysis:
From the truth table, we can observe that:
- When 'S1' and 'S0' are both '0', the input signal 'I' is transmitted to the output line 'D0'.
- When 'S1' is '0' and 'S0' is '1', the input signal 'I' is transmitted to the output line 'D1'.
- When 'S1' is '1' and 'S0' is '0', the input signal 'I' is transmitted to the output line 'D2'.
- When 'S1' and 'S0' are both '1', the input signal 'I' is transmitted to the output line 'D3'.

Conclusion:
From the above analysis, it is clear that with two select lines, we can control the selection of one of the four output channels. Thus, the correct answer is option 'A' (2 select lines) for a 1-to-4 demultiplexer.

Basic S-R Flip-Flop

The basic S-R (Set-Reset) flip-flop is a type of sequential logic circuit that can store one bit of information. It is constructed by cross-coupling two NOR (Negative-OR) gates.

Cross-Coupling of NOR Gates

To understand why the cross-coupling of NOR gates is used to construct an S-R flip-flop, let's first examine the truth table of a NOR gate:

A	B	Output
0	0	1
0	1	0
1	0	0
1	1	0

Set and Reset Inputs

In an S-R flip-flop, the two inputs are called the Set and Reset inputs. When the Set input is high (1), it sets the flip-flop to the high (1) state. Conversely, when the Reset input is high (1), it resets the flip-flop to the low (0) state.

Construction of S-R Flip-Flop

To construct an S-R flip-flop using NOR gates, we connect the output of one NOR gate to the Set input of the other NOR gate, and vice versa. This creates a feedback loop between the two gates, allowing the flip-flop to store information.

Working Principle

1. Initially, both inputs are low (0), and the outputs of both NOR gates are high (1).
2. When the Set input is activated (high), the output of the first NOR gate goes low (0), which is fed back to the Set input of the second NOR gate. This causes the output of the second NOR gate to go high (1), setting the flip-flop to the high state.
3. If the Set input returns to low (0), the flip-flop remains in the high state.
4. Similarly, when the Reset input is activated (high), the output of the second NOR gate goes low (0), which is fed back to the Reset input of the first NOR gate. This causes the output of the first NOR gate to go high (1), resetting the flip-flop to the low state.
5. If the Reset input returns to low (0), the flip-flop remains in the low state.

Summary

In summary, the cross-coupling of NOR gates allows the construction of a basic S-R flip-flop. The Set and Reset inputs control the state of the flip-flop, and the feedback loop between the gates maintains the stored information. This flip-flop is a fundamental building block in digital systems, and its behavior can be further modified and enhanced using additional logic gates.

The Darlington emitter-follower circuit is a configuration of two bipolar transistors that provides high current gain and low output impedance. It is commonly used in applications where a high current is required with low signal distortion. One such application is in the output stage of a TTL (Transistor-Transistor Logic) gate.

The TTL gate is a widely used digital logic family that operates on the principles of transistor switching. It has a low output impedance and can source or sink current to drive other TTL gates or loads. However, the TTL gate has certain limitations in terms of its output current capability.

The Darlington emitter-follower circuit is used in the output stage of a TTL gate to overcome these limitations and enhance its performance. The main advantage of using the Darlington configuration in this application is to increase the output current capability of the TTL gate.

Explanation of the options:

a) Increase its IOL (Option A): The Darlington emitter-follower circuit provides a significant increase in the output current capability of the TTL gate. This is achieved by the high current gain of the Darlington pair, which is the product of the individual current gains of the two transistors. By increasing the output current (IOL), the TTL gate can drive larger loads or drive multiple gates without signal degradation.

b) Reduce its IOH (Option B): The Darlington emitter-follower circuit does not have a significant impact on the high-level output current (IOH) of the TTL gate. The IOH is determined by the characteristics of the input stage of the TTL gate and is not directly affected by the output stage configuration.

c) Increase its speed of operation (Option C): The Darlington emitter-follower circuit does not directly affect the speed of operation of the TTL gate. The speed of operation is primarily determined by the switching characteristics of the input and output stages of the TTL gate, as well as the propagation delay through the internal logic.

d) Reduce power dissipation (Option D): The Darlington emitter-follower circuit may actually increase the power dissipation of the TTL gate. This is due to the additional transistor in the Darlington configuration, which introduces additional voltage drops and losses. However, the increase in power dissipation is usually negligible compared to the benefits gained in terms of increased output current capability.

In conclusion, the Darlington emitter-follower circuit is used in the output stage of a TTL gate to increase its output current capability (IOL). This allows the TTL gate to drive larger loads or multiple gates without signal degradation.

The S-R flip-flop is a fundamental building block in digital electronics, commonly used to store and manipulate binary information. It has two inputs, S (set) and R (reset), and two outputs, Q (output) and Q' (complement of output). The truth table for an S-R flip-flop lists the possible combinations of inputs and their corresponding outputs.

To understand the number of valid entries in the truth table, let's analyze the behavior of the S-R flip-flop. The flip-flop has two stable states: set and reset. When the set input (S) is high and the reset input (R) is low, the flip-flop is set and the output Q is high. Conversely, when the reset input (R) is high and the set input (S) is low, the flip-flop is reset and the output Q is low. When both inputs are high or both inputs are low, the flip-flop enters an undefined state, where the outputs Q and Q' can be unpredictable.

Now, let's construct the truth table for the S-R flip-flop:

| S | R | Q | Q' |
|---|---|---|----|
| 0 | 0 | ? | ? |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | ? | ? |

- Undefined entries:
- When both S and R inputs are low (0), the flip-flop enters an undefined state. This is because the behavior of the flip-flop is not well-defined when both inputs are low. The outputs Q and Q' can be unpredictable, and thus, these entries are marked as undefined in the truth table.

- Valid entries:
- When the S and R inputs are such that one is high (1) and the other is low (0), the flip-flop is in a well-defined state. These are the valid entries in the truth table, as they represent the expected behavior of the flip-flop.
- In these valid entries, the output Q is determined by the set (S) and reset (R) inputs. For example, when S is high and R is low, the flip-flop is set, and thus, the output Q is high (1).

Therefore, the truth table for an S-R flip-flop has 3 valid entries, corresponding to the combinations of inputs that result in a well-defined state. These entries are:

| S | R | Q | Q' |
|---|---|---|----|
| 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | ? | ? |

Hence, the correct answer is option 'C' - 3 valid entries.