3. Use D flip-flops to design a counter with the following repeated binary sequence: 1, 3, 7, 5, 11, 9, 13, 15. Use don't care states as appropriate.
3. Use D flip-flops to design a counter with the following repeated binary sequence: 1, 3, 7, 5, 11, 9, 13, 15. Use don't care states as appropriate.
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![### Design of a Counter using D Flip-Flops
**Problem Statement:**
3. Use D flip-flops to design a counter with the following repeated binary sequence:
1, 3, 7, 5, 11, 9, 13, 15.
Use *don't care* states as appropriate.
**Solution Approach:**
To design the counter using D flip-flops, follow these steps:
1. **State the Binary Sequence:** Write down the provided binary sequence:
- 1 (0001)
- 3 (0011)
- 7 (0111)
- 5 (0101)
- 11 (1011)
- 9 (1001)
- 13 (1101)
- 15 (1111)
2. **Create a State Table:** Develop a state table for the counter showing the present states and the next states in the binary sequence.
3. **Construct Flip-Flop Excitation Table:** Use the state table to determine the necessary input conditions for the D flip-flops.
4. **Design the Circuit:** Draw the logic circuit diagram using the excitation functions derived from the excitation table.
5. **Handling Don't Care States:** Employ don't care conditions in the Karnaugh maps while simplifying the Boolean expressions.
**State Table:**
| Present State | Next State |
|:-------------:|:----------:|
| 0001 | 0011 |
| 0011 | 0111 |
| 0111 | 0101 |
| 0101 | 1011 |
| 1011 | 1001 |
| 1001 | 1101 |
| 1101 | 1111 |
| 1111 | 0001 |
**Excitation Table for D Flip-Flops:**
(D0, D1, D2, and D3 are the inputs to the D flip-flops.)
Using the state table, determine the inputs required to transition between states:
- For D0, D1, D2, and D3, use the next state values directly as the input since a D flip-flop is used.
**Example Transitions:**
| Flip-Flop | Present State | Next State |
|:---------:|:-------------:|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5646b139-543d-4164-b214-191929b49dde%2F189c2ab8-c400-4516-93d5-766a5a53c92c%2Fqbp4g8f_processed.png&w=3840&q=75)
Transcribed Image Text:### Design of a Counter using D Flip-Flops
**Problem Statement:**
3. Use D flip-flops to design a counter with the following repeated binary sequence:
1, 3, 7, 5, 11, 9, 13, 15.
Use *don't care* states as appropriate.
**Solution Approach:**
To design the counter using D flip-flops, follow these steps:
1. **State the Binary Sequence:** Write down the provided binary sequence:
- 1 (0001)
- 3 (0011)
- 7 (0111)
- 5 (0101)
- 11 (1011)
- 9 (1001)
- 13 (1101)
- 15 (1111)
2. **Create a State Table:** Develop a state table for the counter showing the present states and the next states in the binary sequence.
3. **Construct Flip-Flop Excitation Table:** Use the state table to determine the necessary input conditions for the D flip-flops.
4. **Design the Circuit:** Draw the logic circuit diagram using the excitation functions derived from the excitation table.
5. **Handling Don't Care States:** Employ don't care conditions in the Karnaugh maps while simplifying the Boolean expressions.
**State Table:**
| Present State | Next State |
|:-------------:|:----------:|
| 0001 | 0011 |
| 0011 | 0111 |
| 0111 | 0101 |
| 0101 | 1011 |
| 1011 | 1001 |
| 1001 | 1101 |
| 1101 | 1111 |
| 1111 | 0001 |
**Excitation Table for D Flip-Flops:**
(D0, D1, D2, and D3 are the inputs to the D flip-flops.)
Using the state table, determine the inputs required to transition between states:
- For D0, D1, D2, and D3, use the next state values directly as the input since a D flip-flop is used.
**Example Transitions:**
| Flip-Flop | Present State | Next State |
|:---------:|:-------------:|
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