Step1/8

Answer :

---> (a) To implement a ripple counter that loops the sequence 0-1-2-3-4-5-6-7-0, we need a 3-bit counter, which can count from 0 to 7. We can use three positive-edge triggered D flip-flops and connect their outputs as follows:

The Q output of the first flip-flop (FF1) is connected to the D input of the second flip-flop (FF2).

The Q output of the second flip-flop (FF2) is connected to the D input of the third flip-flop (FF3).

The Q output of the third flip-flop (FF3) is connected to the D input of the first flip-flop (FF1), and also to the input of an AND gate.

The outputs of the three flip-flops are also connected to an OR gate, whose output is used as the clock input for all three flip-flops.

Step2/8

--> The AND gate is used to reset the counter to 0 when it reaches 7. When the counter reaches 7, the Q outputs of the three flip-flops will be 1, 1, and 1, respectively.

This will cause the AND gate to output a high signal, which will be fed back to the first flip-flop's D input, forcing it to reset to 0 on the next clock cycle.

The OR gate ensures that all three flip-flops are triggered by the same clock signal.

Step3/8

---> The logic circuit diagram for the ripple counter is shown below:

Step4/8

---> (b) To modify the ripple counter to loop the sequence 0-7-6-5, we need to change the connections between the flip-flops. The modified circuit can be implemented as follows:

The Q output of the first flip-flop (FF1) is connected to the D input of the second flip-flop (FF2).

The Q' (inverted Q) output of the second flip-flop (FF2) is connected to the D input of the third flip-flop (FF3).

The Q' output of the third flip-flop (FF3) is connected to the D input of the first flip-flop (FF1), and also to the input of an AND gate.

The outputs of the three flip-flops are also connected to an OR gate, whose output is used as the clock input for all three flip-flops.

Step5/8

--> The AND gate is used to reset the counter to 0 when it reaches 5. When the counter reaches 5, the Q' output of the third flip-flop will be 0, which will cause the AND gate to output a high signal that will be fed back to the first flip-flop's D input, forcing it to reset to 0 on the next clock cycle.

The OR gate ensures that all three flip-flops are triggered by the same clock signal.

Step6/8

----> The logic circuit diagram for the modified ripple counter is shown below:

Step7/8

Note that the connections between the flip-flops have been changed, such that the first flip-flop's output (Q) is connected to the second flip-flop's input (D), and the third flip-flop's output (Q') is connected to the first flip-flop's input (D).

This allows us to loop through the sequence 0-7-6-5, instead of 0-1-2-3-4-5-6-7-0. The AND gate is still used to reset the counter to 0 when it reaches 5, as before.

Step8/8

------> The modified sequence operates as follows:

1. Initially, all flip-flop outputs are 0.

2. On the first clock pulse, the first flip-flop's input (D) is set to 0 (Q' of the third flip-flop), while the other flip-flop inputs remain 0. When the clock edge occurs, the first flip-flop's output (Q) becomes 0, the second flip-flop's output becomes 0, and the third flip-flop's output becomes 1.

3. On the second clock pulse, the second flip-flop's input is set to 1 (Q of the first flip-flop), while the other flip-flop inputs remain 0. When the clock edge occurs, the first flip-flop's output becomes 1, the second flip-flop's output becomes 1, and the third flip-flop's output becomes 0.

4. On the third clock pulse, the second flip-flop's input is set to 0 (Q' of the third flip-flop), while the other flip-flop inputs remain 0. When the clock edge occurs, the first flip-flop's output becomes 0, the second flip-flop's output becomes 0, and the third flip-flop's output becomes 1.

5. On the fourth clock pulse, the third flip-flop's input is set to 1 (Q of the first flip-flop), while the other flip-flop inputs remain 0. When the clock edge occurs, the first flip-flop's output becomes 1, the second flip-flop's output becomes 1, and the third flip-flop's output becomes 1.

6. On the fifth clock pulse, the third flip-flop's input is set to 0 (Q' of the third flip-flop), while the other flip-flop inputs remain 0. When the clock edge occurs, the first flip-flop's output becomes 0, the second flip-flop's output becomes 1, and the third flip-flop's output becomes 0.

7. On the sixth clock pulse, the second flip-flop's input is set to 1 (Q of the first flip-flop), while the other flip-flop inputs remain 0. When the clock edge occurs, the first flip-flop's output becomes 1, the second flip-flop's output becomes 0, and the third flip-flop's output becomes 1.

8. On the seventh clock pulse, the second flip-flop's input is set to 0 (Q' of the third flip-flop), while the other flip-flop inputs remain 0. When the clock edge occurs, the first flip-flop's output becomes 0, the second flip-flop's output becomes 1, and the third flip-flop's output becomes 0.

9. The counter then repeats the sequence from step 2 onwards.

Note that the modified ripple counter only requires three flip-flops instead of four, since we are only counting up to 7 instead of 15.

Explanation:

Answer :

--> A ripple counter is a type of digital circuit that uses flip-flops to count a sequence of binary values. By connecting the outputs of the flip-flops to the inputs of the next stage, the counter can increment through the binary sequence on each clock pulse. In this task, we were asked to design two ripple counters using positive-edge triggered D flip-flops.

For the first part, we designed a ripple counter that loops through the sequence 0-1-2-3-4-5-6-7-0. This counter required four flip-flops to count up to the value 7, and an AND gate was used to reset the counter to 0 when it reached the value 7.

For the second part, we modified the counter to loop through the sequence 0-7-6-5 instead. This counter only required three flip-flops, and an AND gate was used to reset the counter to 0 when it reached the value 5. The connections between the flip-flops were changed to achieve the desired sequence.

Overall, ripple counters are an important building block in digital circuits and can be used in a wide range of applications, such as frequency dividers, digital clocks, and programmable logic devices.

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