Question

Implement T flip-flop using JK flip-flop. Write its truth table.

Answer 1

### T Flip-Flop Using JK Flip-Flop

A **T flip-flop** (Toggle flip-flop) changes its state when the input \( T = 1 \), and holds its previous state when \( T = 0 \). We can implement a T flip-flop using a JK flip-flop by appropriately connecting the \( J \) and \( K \) inputs.

### JK Flip-Flop Recap

The truth table for a JK flip-flop is as follows:

| \( J \) | \( K \) | Next State (Qₙ₊₁) |
|--------|--------|--------------------|
| 0      | 0      | \( Q_n \) (No change) |
| 0      | 1      | 0 (Reset)           |
| 1      | 0      | 1 (Set)             |
| 1      | 1      | \( \overline{Q_n} \) (Toggle) |

### T Flip-Flop Using JK Flip-Flop

To implement the T flip-flop behavior using a JK flip-flop, we need to connect the inputs \( J \) and \( K \) in such a way that they can:

1. **Hold the current state** when \( T = 0 \),
2. **Toggle the state** when \( T = 1 \).

#### Connection:

- Connect \( J = T \) and \( K = T \).

This configuration ensures that the JK flip-flop behaves like a T flip-flop, as follows:
- When \( T = 0 \), both \( J = 0 \) and \( K = 0 \), and the JK flip-flop will **hold its current state** (no change).
- When \( T = 1 \), both \( J = 1 \) and \( K = 1 \), and the JK flip-flop will **toggle** its current state.

### Truth Table for T Flip-Flop Using JK Flip-Flop

| Current State \( Q_n \) | T (Input) | Next State \( Q_{n+1} \) | Explanation               |
|-------------------------|-----------|--------------------------|---------------------------|
| 0                       | 0         | 0                        | No change (Hold current state) |
| 1                       | 0         | 1                        | No change (Hold current state) |
| 0                       | 1         | 1                        | Toggle (Flip to 1)         |
| 1                       | 1         | 0                        | Toggle (Flip to 0)         |

### Explanation:
- When \( T = 0 \), the flip-flop holds the current state, whether it is 0 or 1.
- When \( T = 1 \), the flip-flop toggles its state: 0 becomes 1, and 1 becomes 0.

This setup effectively replicates the behavior of a T flip-flop using a JK flip-flop by utilizing the toggle characteristic of the JK flip-flop.

Answer 2

To implement a T Flip-Flop using JK Flip-Flop, you can connect the T Flip-Flop input to both J and K inputs of the JK Flip-Flop. This configuration leverages the JK Flip-Flop's characteristic behavior to mimic a T Flip-Flop's behavior.

### JK Flip-Flop Basics

A JK Flip-Flop is a versatile type of flip-flop where:

- **J** input is the set input.
- **K** input is the reset input.
- **Q** is the output.
- **Q'** is the complement of Q.
- **CLK** is the clock input.

The behavior of a JK Flip-Flop can be summarized in its truth table:

| J | K | Q (next) |
|---|---|----------|
| 0 | 0 | Q (no change) |
| 0 | 1 | 0 (reset) |
| 1 | 0 | 1 (set) |
| 1 | 1 | Q' (toggle) |

### T Flip-Flop Using JK Flip-Flop

For a T Flip-Flop:

- **T** input is connected to both J and K inputs of the JK Flip-Flop.

The behavior of the T Flip-Flop is such that it toggles its state when the T input is high and holds its state when T is low.

### Truth Table for T Flip-Flop Using JK Flip-Flop

| T | Q (current) | Q (next) |
|---|-------------|----------|
| 0 | 0           | 0        |
| 0 | 1           | 1        |
| 1 | 0           | 1        |
| 1 | 1           | 0        |

### Explanation

- **When T = 0**: The JK Flip-Flop behaves like a JK Flip-Flop with J = 0 and K = 0, meaning the output does not change.
- **When T = 1**: The JK Flip-Flop behaves like a JK Flip-Flop with J = 1 and K = 1, meaning the output toggles its state on each clock pulse.

Thus, by connecting the T input to both J and K of the JK Flip-Flop, the JK Flip-Flop essentially behaves like a T Flip-Flop, toggling its output state with each clock pulse when T is high.