D Flip-Flop:
Functioning:
A D flip-flop, or Data flip-flop, is a type of digital storage element that stores and outputs the value of the D (data) input when the clock signal transitions from one state to another (typically rising or falling edge). The logic diagram for a D flip-flop and its characteristic table are as follows:
Logic Diagram:
```
+-----+
D ---->| |
| D |---- Q
CLK--->| F |
| F |---- Q'
| L |
+-----+
```
- \( D \): Data input
- \( Q \): Output
- \( Q' \): Complement of output
- \( CLK \): Clock input
Characteristic Table:
```
| CLK | D | Q(t) | Q(t+1) |
|-----|---|------|--------|
| ↑ | | 0 | D |
| ↑ | | 1 | D |
```
- On the rising edge of the clock (\(CLK\)), the output \(Q(t+1)\) becomes the value of the data input \(D\) at that moment.
Excitation Table:
```
| CLK | D | Q(t) | Q'(t) |
|-----|---|------|-------|
| ↑ | 0 | 0 | 1 |
| ↑ | 1 | 1 | 0 |
```
- The excitation table describes the inputs that will cause a change in the state of the flip-flop.
T Flip-Flop:
Functioning:
A T flip-flop, or Toggle flip-flop, changes its state (toggles) when the clock signal transitions and the T (toggle) input is 1. The logic diagram and characteristic table for a T flip-flop are as follows:
Logic Diagram:
```
+-----+
T ---->| |
| T |---- Q
CLK--->| F |
| F |---- Q'
| L |
+-----+
```
- \( T \): Toggle input
Characteristic Table:
```
| CLK | T | Q(t) | Q(t+1) |
|-----|---|------|--------|
| ↑ | 0 | 0 | 0 |
| ↑ | 0 | 1 | 1 |
| ↑ | 1 | 0 | ~Q |
| ↑ | 1 | 1 | ~Q |
```
- On the rising edge of the clock (\(CLK\)):
- If \(T = 0\), the output remains the same.
- If \(T = 1\), the output toggles (\(~Q\) becomes \(Q\) and vice versa).
Excitation Table:
```
| CLK | T | Q(t) | Q'(t) |
|-----|---|------|-------|
| ↑ | 0 | 0 | 1 |
| ↑ | 0 | 1 | 0 |
| ↑ | 1 | 0 | 1 |
| ↑ | 1 | 1 | 0 |
```
- The excitation table describes the inputs that will cause a change in the state of the flip-flop.
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