The correct answer is: 2) the output of the previous flip-flop

Explanation:
In an asynchronous counter (also called a ripple counter):

Only the first flip-flop receives the external clock signal.

Each subsequent flip-flop is triggered by the output (Q or Q̅) of the previous flip-flop, not by a common clock.

This causes a ripple effect, where changes propagate sequentially, leading to a slight delay between stages.

Additional Information
Asynchronous Counter

Asynchronous counters are those counters where the clock of the next stage is obtained from the output of the previous state.

The correct answer is option 3) 1

Concept:

Let's analyze the given problem statement and options in detail:

Given:

• T = 1
• Current output Q = 0

Let's analyze the state of Q after each clock pulse:

1. Initial state Q = 0
2. After 1st clock pulse: Q will toggle from 0 to 1
3. After 2nd clock pulse: Q will toggle from 1 to 0
4. After 3rd clock pulse: Q will toggle from 0 to 1

Therefore, the output Q after 3 clock pulses will be 1.

Concept:

Serial input serial output:

SISO is used to provide 'n' clock pulses delay to the input data 

If 'T' is clock pulses time period then  delay provided by n bit SISO is "nT"

n bit register to enter n bit data it required n clock pulses in serial form.

Output is taken serially than (n-1) clock pulses are required

The correct answer is Option 2.

Key Points

• Knowledge base designing involves a specific sequence of steps to accurately represent a domain of interest.
  • A. Ask questions about the intended interpretation: This step involves understanding the context and the specific meanings of the propositions that will be represented in the knowledge base.
  • B. Choose task domain or world to represent: This step involves selecting the particular area or world that the knowledge base will cover.
  • C. Select atoms to represent propositions of interest: In this step, the basic atomic elements or propositions that are relevant to the domain are identified.
  • D. Tell the system propositions that are true in the intended interpretation/axiomatizing the domain: This step involves defining the truths or axioms that apply to the chosen domain.

The correct sequence of these steps is:

1. B. Choose task domain or world to represent.
2. C. Select atoms to represent propositions of interest.
3. D. Tell the system propositions that are true in the intended interpretation/axiomatizing the domain.
4. A. Ask questions about the intended interpretation.

Hence, the correct answer is Option 2.

Additional Information

• The steps in knowledge base designing ensure that the system accurately represents the chosen domain and can effectively interpret and answer queries.
• Each step builds upon the previous ones, creating a robust and reliable knowledge base.
• Properly asking questions about the intended interpretation helps in refining the knowledge base and ensuring it accurately reflects the domain.

Concept:

Right Shift Register:

• The shift register, which allows serial input (one bit after the other through a single data line) and produces a serial output is known as Serial-In Serial-Out shift register.
• Since there is only one output, the data leaves the shift register one bit at a time in a serial pattern, thus the name Serial-In Serial-Out Shift Register.

Solution:

Explanation:

Latches and Flip-Flop:

• Latches and flip-flops are the basic elements to store 1-bit of data. Hence they are also known as a one-bit memory element.
• Latches change the output continuously when there is a change in the input, i.e. they are level triggered.
• Flip-flop is a combination of latch and clock. It changes the output that is adjusted by the clock.
• The main difference between a latch and a flip-flop is that a flip-flop has a clock signal, whereas a latch does not.
• We can say that a flip-flop without a clock is a latch.
• Latches are asynchronous, which means that the output of a latch depends on its input.
• Basically, there are 4 types of latches: SR latch, JK latch, D latch, T latch.

T flip flop

The "T Flip Flop" has only one input.

It has only two output states i.e. hold and toggle.

For T = 0, the output is Q_n (Hold state)

For T = 1, the output is \(\overline{Q_n}\) (Toggle state)

The output equation of the T flip-flop is:

Q_n+1 = T ⊗ Q_n

Concept:

A Johnson counter is a modified ring counter, where the inverted output from the last flip flop is connected to the input to the first.

The MOD of the Johnson counter is 2n if n flip-flops are used.

The circuit diagram for a 4-bit Johnson Counter is as shown:

Calculation:

Total number of states in 4-bit counter are: 2ⁿ = 2⁴ = 16

Total states in Johnson counter are: 2n = 2.(4) = 8

D flip flop:

D flip flop has only one input terminal. The output of the D flip flop will be the same as the input. Hence, it is used in delay circuits.

The circuit is as shown below.

Logic symbol:

Truth table:

Characteristic equation: Qn+1 = D

The D flip flop may be obtained from an S-R flip flop by just putting one inverter between the S and R as shown in the figure below.

S = R̅

The D flip flop may be obtained from a J-K flip flop by just putting one inverter between the J and K as shown in the figure below.

K = J̅

T flip flop:

T flip flop has only one input terminal. The output of the T flip flop will be toggled when the input is high on every new clock pulse. The output will be the same as the previous state when the input is low.

The circuit is as shown below.

Logic symbol:

Truth table:

Characteristic equation: Qn+1 = TQ̅­n + T̅Qn

The T flip flop may be obtained from a J-K flip flop by making both the inputs are the same i.e. J = K.

The correct answer is option 2): 4

Concept:

For a counter with ‘n’ flip flops:

• The total number of states = 2ⁿ (0 to 2ⁿ – 1)
• The largest number that can be stored in the counter = 2ⁿ – 1
• To construct a counter with any MOD number, the minimum number of flip flops required must  satisfy: Modulus ≤ 2ⁿ
• Where n is the number of flip-flops and is the minimum value satisfying the above condition.
• Note: A MOD-N counter is also called as a divide by N counter as the input frequency is divided by the number of states of the counter.

Calculation:

Number no. of flip – flops are required to construct mod-12 counter,

must satisfy: 2ⁿ ≥ 12 The minimum value of n satisfying the above is: n = 4

• Latches and flip-flops are the basic elements for storing information. They are made of logic gates.
• One latch or flip-flop can store a 1-bit of information.
• For latches, its input can affect the output as long as the enable signal is asserted (high).
• For flip-flop, its input can affect the output only when the enable signal changes (falling edge or rising edge).

The difference between latches and flip flops is shown

Concept:

For a counter with ‘n’ flip flops:

• The total number of states = 2n (0 to 2n – 1)
• The largest number that can be stored in the counter = 2n – 1

To construct a counter with any MOD number, the minimum number flip flops required must satisfy:

Modulus ≤ 2n

Where n is the number of flip-flops and is the minimum value satisfying the above condition.

Calculation:

The total number of states required when n = 3:

23  ≥  8

The states will vary from (0 to 7)

So the maximum states possible for the counter will be 8.

Concept:

For a counter with ‘n’ flip flops:

• The total number of states = 2n (0 to 2n – 1)
• The largest number that can be stored in the counter = 2n – 1

To construct a counter with any MOD number, the minimum number flip flops required must satisfy:

Modulus ≤ 2n

Where n is the number of flip-flops and is the minimum value satisfying the above condition.

Calculation:

Given: 

n = 3

Modulus ≤ 2n

Modulus ≤ 2³

Modulus ≤ 8

The most appropriate answer is option 1 i.e. Mod 6.

Johnson Counter: 

A Johnson counter is a modified ring counter, where the inverted output from the last flip flop is connected to the input to the first.

The circuit diagram for a 4-bit Johnson Counter is as shown:

The MOD of the Johnson counter is 2n if n flip-flops are used.

For an n-bit counter, the total number of states possible is 2ⁿ. ∴ The number of unused states for a Johnson counter will be:

Unused = Total States possible - Mod of the counter

= 2n - 2n

The correct answer is option 4):(Multiplexer)

Concept:

• Combinational logic is a type of digital logic that is implemented by Boolean circuits, where the output is a pure function of the present input only.
• Sequential logic is a type of digital logic in which the output depends not only on the present input but also on the history of the output.
• Sequential logic has memory while combinational logic does not.
• Flip-flop, counter, and shift registers are sequential circuits whereas multiplexer, decoder, and encoder act like combinational circuits.
•  A multiplexer also known as a data selector, is a device that selects between several analog or digital input signals and forwards the selected input to a single output line. The selection is directed by a separate set of digital inputs known as select lines.
• The Multiplexer has shown as 

​

Additional Information

•  A flip-flop is a sequential digital electronic circuit having two stable states that can be used to store one bit of binary data. Flip-flops are the fundamental building blocks of all memory devices.
• The counter is a sequential circuit consisting of a set of flip-flops which can go through a sequence of states. It is used to count the number of clock cycles. Since the clock pulses occur at known intervals, the counter can be used for measuring time such as period or frequency.
• A shift register is a type of digital circuit using a cascade of flip-flops where the output of one flip-flop is connected to the input of the next. They share a single clock signal, which causes the data stored in the system to shift from one location to the next.