All questions of Digital Logic for Computer Science Engineering (CSE) Exam

Components of a Frequency Counter

Frequency counters are electronic devices used to measure the frequency of an input signal. They are commonly used in various applications such as telecommunications, electronics, and research. A frequency counter typically consists of several components that work together to accurately measure and display the frequency of a signal.

The components of a frequency counter include:

1. Accurate Timebase:
- An accurate timebase is a crucial component of a frequency counter.
- It provides a stable and precise reference signal for counting the input frequency.
- It is usually generated by a crystal oscillator or a temperature-compensated oscillator.
- The timebase determines the resolution and accuracy of the frequency counter.

2. Decade Divider:
- A decade divider is used to divide the input frequency down to a manageable range.
- It divides the input frequency by powers of ten, allowing the counter to operate within its counting range.
- The divided frequency is then used as the input for the counter/latch.

3. Counter/Latch:
- The counter/latch is the main component responsible for counting the input signal.
- It counts the number of input cycles within a specific time period.
- The counted value is then stored in a latch for display.

4. Display:
- The display is an essential component of a frequency counter.
- It shows the measured frequency to the user.
- The display can be in the form of a digital readout or an analog display.

Explanation:
Among the given options, the component that is not a part of a frequency counter is the "Encoder" (option D). An encoder is not typically found in a frequency counter.

- An encoder is a device used to convert an analog or digital signal into a different format.
- It is commonly used in applications such as encoding data, controlling motor movements, or generating position feedback.
- However, it is not directly involved in the measurement or counting of frequencies in a frequency counter.

Therefore, the correct answer is option D, "Encoder."

The frequency at which digital data can be applied to a gate is the operating frequency.



Digital data refers to the discrete representation of information in binary code, where signals are represented by a series of 0s and 1s. These digital signals are processed by electronic devices such as gates, which are the basic building blocks of digital circuits.


The operating frequency is the frequency at which a digital circuit or device is designed to function optimally. It determines the speed at which data can be processed and transferred within the circuit. In the context of applying digital data to a gate, the operating frequency represents the rate at which the gate can accept and process incoming digital signals.

Reasons for choosing option 'C' (Operating frequency):
1. Run-time frequency: The term "run-time frequency" is not commonly used in the context of digital circuits or gates. It does not specifically refer to the frequency at which digital data is applied to a gate.
2. Propagation Frequency: Propagation frequency is related to the delay or time taken for a signal to propagate through a circuit. It is not directly related to the frequency at which digital data is applied to a gate.
3. AC frequency: AC frequency generally refers to the frequency of alternating current, which is not directly relevant to the frequency at which digital data is applied to a gate.


The correct answer is option 'C' (Operating frequency) because it represents the frequency at which digital data can be applied to a gate. The operating frequency determines the speed and efficiency of digital circuits in processing and transferring data.

IB, the base current.

The base current (IB) can be calculated using the equation:

IB = IC - IE

Substituting the given values:

IB = 110 mA - 55 mA

IB = 55 mA

BCD stands for Binary Coded Decimal. It is a form of representing decimal numbers using a binary code. In BCD, each decimal digit is represented by a 4-bit binary code. Let's break down the answer and explain why it is option 'B' - 4 bits.

Binary Coded Decimal (BCD)

BCD is a way of representing decimal digits using a binary code. In BCD, each decimal digit is represented by a 4-bit binary code. This means that 4 binary bits are required to represent a single BCD digit.

Binary Digits

In binary representation, each digit can take on one of two values, 0 or 1.

Decimal Digits

In decimal representation, each digit can take on one of ten values, from 0 to 9.

BCD Representation

To represent decimal digits using BCD, each decimal digit is divided into its binary equivalent. For example, the decimal digit 0 is represented as 0000 in BCD, 1 as 0001, 2 as 0010, and so on up to 9 as 1001.

Number of Bits for a BCD Digit

Since each decimal digit is represented by a 4-bit binary code in BCD, we can conclude that 4 bits are required to store one BCD digit.

Examples

Let's consider some examples to further illustrate this:

- The BCD representation of the decimal digit 3 is 0011, which requires 4 bits.
- The BCD representation of the decimal digit 7 is 0111, which also requires 4 bits.
- The BCD representation of the decimal digit 9 is 1001, again requiring 4 bits.

Conclusion

In conclusion, 4 bits are required to store one BCD digit. This is because each decimal digit is represented by a 4-bit binary code in BCD. Therefore, the correct answer is option 'B' - 4 bits.

Conversion of Hexadecimal to Octal

To convert a hexadecimal number to an octal number, we need to follow the following steps:

Step 1: Write down the hexadecimal number

The given hexadecimal number is (1E.43)16

Step 2: Convert the fractional part to decimal

The fractional part is .43

.43 × 16 = 6.88

The integer part is 6.

Step 3: Convert the integer part to binary

1E = 0001 1110

Step 4: Group the binary digits into sets of three

000 111 0

Step 5: Convert each set of three binary digits to octal

0 7 0

Step 6: Combine the octal digits

The final answer is (36.206)8

X 10^12 metres
b) 2.8968192 x 10^11 metres
c) 2.8968192 x 10^13 metres
d) 2.8968192 x 10^14 metres

Answer: c) 2.8968192 x 10^13 metres

Explanation:

To calculate the number of states or bit patterns in an 8-bit Johnson counter sequence, we need to understand the concept of a Johnson counter and its sequence.

A Johnson counter is a modified version of a ring counter. It is a sequential circuit that cycles through a fixed sequence of states. In an 8-bit Johnson counter, there are 8 flip-flops connected in a ring, forming a circular shift register.

Johnson Counter Sequence:
The sequence of states in a Johnson counter follows a specific pattern. It starts with all bits set to 0 and then cycles through a sequence of 2^n - 1 states, where n is the number of bits in the counter.

In an 8-bit Johnson counter, the sequence will have 2^8 - 1 = 255 states. However, we need to exclude the initial state (all bits set to 0) from the count.

Therefore, the number of states in the Johnson counter sequence is 255 - 1 = 254.

Orbit Patterns:
An orbit pattern is a subset of the Johnson counter sequence that represents a complete cycle or loop. It starts and ends at the same state.

To calculate the number of orbit patterns, we need to find the number of states in each orbit pattern. In an 8-bit Johnson counter, each orbit pattern will have 8 states, as it takes 8 clock cycles for the counter to return to its initial state.

The total number of possible orbit patterns can be calculated by dividing the total number of states in the Johnson counter sequence by the number of states in each orbit pattern.

Total number of states = 254
Number of states in each orbit pattern = 8

Number of orbit patterns = Total number of states / Number of states in each orbit pattern
= 254 / 8
= 31.75

Since the number of orbit patterns cannot be a fraction, we round it down to the nearest whole number.

Therefore, the number of orbit patterns in an 8-bit Johnson counter sequence is 31.

Conclusion:
The correct answer is option A) 240.

None of the options are equal to 1.

D Flip Flop from J-K Flip Flop

D flip flop is a fundamental building block in digital circuits, which is used to store a single bit of data. It has a single input called the data input (D), which controls the state of the flip flop. The output of the flip flop is the state of the stored data. A D flip flop can be realized from a J-K flip flop by connecting the J and K inputs together and feeding the same input to both of them.

Explanation

The J-K flip flop has two inputs, J (set) and K (reset), and two outputs, Q (state) and Q' (complement). It can store one bit of information and has two stable states: SET and RESET. When J=K=0, the flip flop maintains its current state. When J=K=1, the flip flop toggles its state. When J=1 and K=0, the flip flop sets its state to 1. When J=0 and K=1, the flip flop resets its state to 0.

To convert a J-K flip flop into a D flip flop, we need to connect the J and K inputs together and feed the same input to both of them. This means that J=K=D. The truth table for the D flip flop is as follows:

D | Q | Q'
--|---|---
0 | 0 | 1
1 | 1 | 0

To implement this truth table using a J-K flip flop, we can connect the D input to both the J and K inputs of the flip flop. This means that J=K=D. The truth table for the J-K flip flop with J=K=D is as follows:

D | Q | Q'
--|---|---
0 | 0 | 0
1 | 1 | 1

As we can see, the truth table for the J-K flip flop with J=K=D is the same as the truth table for the D flip flop. Therefore, a D flip flop can be implemented using a J-K flip flop by connecting the J and K inputs together and feeding the same input to both of them.

JK Flip-Flop in Toggle Mode:

Explanation:
A JK flip-flop is a sequential circuit element that can store one bit of information. It has two inputs, J (set) and K (reset), and two outputs, Q (output) and Q' (complement of output). The behavior of a JK flip-flop depends on the inputs and the state of the flip-flop.

In toggle mode, the output of a JK flip-flop toggles (changes state) whenever both J and K inputs are high (1). The flip-flop retains its current state when both J and K inputs are low (0). The toggle mode is also known as the "flip-flop" mode or "T" mode.

Options:
Let's analyze the given options:

a) J = 0, K = 1:
When J = 0 and K = 1, the flip-flop operates in the "reset" mode. The output Q will be 0, regardless of its previous state. This option does not represent the toggle mode.

b) J = 1, K = 1:
When J = 1 and K = 1, the flip-flop operates in the "toggle" mode. The output Q will toggle (change state) with each clock pulse. This option represents the toggle mode correctly.

c) J = 0, K = 0:
When J = 0 and K = 0, the flip-flop retains its current state. The output Q will remain unchanged, regardless of its previous state. This option does not represent the toggle mode.

d) J = 1, K = 0:
When J = 1 and K = 0, the flip-flop operates in the "set" mode. The output Q will be forced to 1, regardless of its previous state. This option does not represent the toggle mode.

Conclusion:
From the given options, option 'B' (J = 1, K = 1) represents the correct input values for a JK flip-flop to operate in the toggle mode. In this mode, the output Q will toggle (change state) with each clock pulse.

Universal Gates Explained
Universal gates are fundamental in digital electronics, capable of implementing any Boolean function without the need for other types of gates. The two primary universal gates are NAND and NOR.

Why NAND and NOR are Universal Gates
- **Functionality**: Both NAND and NOR can create all basic logic operations:
- **AND**:
- NAND gate can be used to create an AND operation by negating its output.
- **OR**:
- NOR gate can create an OR operation by negating its output.
- **NOT**:
- Each gate can also function as a NOT gate through proper configuration.
- **Combination**: By combining multiple NAND or NOR gates, any logical expression can be formed:
- For example, a two-input NAND gate's output is true unless both inputs are true. By feeding this output back into other gates, complex logic can be designed.

Comparison with Other Gates
- **XOR**: While useful in specific contexts, it cannot alone produce all logic functions and is not a universal gate.
- **AND/OR**: These gates cannot independently form all functions; they require NOT gates to achieve universality.

Conclusion
- Since NAND and NOR can independently form any logic circuit, they are classified as universal gates. This versatility makes them essential in digital circuit design, simplifying the creation of complex logic systems. Thus, the correct answer to the question is option 'D': NOR and NAND.