Question

Construct a 3-bit synchronous UP counter using flip-flop. Also, draw its timing diagram.

Answer 1

To construct a 3-bit synchronous up counter using flip-flops, follow these steps:

### Components:
1. **3 JK Flip-Flops** (or D flip-flops, but JK is common for counters)
2. **Clock Signal**
3. **Logic Gates** (for JK flip-flops: AND, OR, NOT gates)

### Steps to Construct the Counter:

1. **Flip-Flops Setup:**
   - **FF0**: Least significant bit (Q0)
   - **FF1**: Middle bit (Q1)
   - **FF2**: Most significant bit (Q2)

2. **Connect the Clock Signal:**
   - All flip-flops receive the same clock signal, ensuring synchronous operation.

3. **Connect JK Inputs for Flip-Flops:**
   - **FF0**: J0 = 1, K0 = 1 (Toggle mode)
   - **FF1**: J1 = Q0, K1 = \(\overline{Q0}\)
   - **FF2**: J2 = Q1 \& Q0, K2 = \(\overline{Q1} \& Q0\)

4. **Logic Gates Configuration:**
   - **FF1’s J input**: Connected to Q0
   - **FF1’s K input**: Connected to \(\overline{Q0}\)
   - **FF2’s J input**: Connected to Q0 \& Q1 (AND gate)
   - **FF2’s K input**: Connected to \(\overline{Q1} \& Q0\) (AND gate with a NOT gate for \(\overline{Q1}\))

### Timing Diagram:

1. **Clock Pulse**: This is a square wave signal that synchronizes the flip-flops.
2. **Q0**: Flips on every clock pulse.
3. **Q1**: Flips every two clock pulses.
4. **Q2**: Flips every four clock pulses.

#### Example Timing Diagram:

- **Clock**: A continuous square wave.
- **Q0**: Alternates between 0 and 1 every clock pulse.
- **Q1**: Changes state every two clock pulses.
- **Q2**: Changes state every four clock pulses.

**Timing Diagram Summary:**

| Clock | Q2 | Q1 | Q0 |
|-------|----|----|----|
| 0     | 0  | 0  | 0  |
| 1     | 0  | 0  | 1  |
| 2     | 0  | 1  | 0  |
| 3     | 0  | 1  | 1  |
| 4     | 1  | 0  | 0  |
| 5     | 1  | 0  | 1  |
| 6     | 1  | 1  | 0  |
| 7     | 1  | 1  | 1  |
| 8     | 0  | 0  | 0  |

This pattern repeats every 8 clock pulses.

Feel free to ask if you need a more detailed explanation or a specific part of the circuit!

Answer 2

A 3-bit synchronous up counter can be constructed using three flip-flops. Each flip-flop will represent a bit of the counter. Here’s a step-by-step guide on how to design this counter and its timing diagram.

### Components Required
1. **3 T Flip-Flops (TFF)** or **JK Flip-Flops** (configured as TFF)
2. **Logic Gates** (AND, OR, NOT) for the flip-flop inputs
3. **Clock Signal** (shared by all flip-flops)

### Design Steps

#### 1. **3-Bit Synchronous Up Counter using T Flip-Flops**

Each T flip-flop will be connected such that the output of one flip-flop is used to control the next.

**Truth Table for T Flip-Flop:**

| T | Q (Next State) |
|---|----------------|
| 0 | Q (No Change)  |
| 1 | Q' (Toggle)    |

**Connections:**
- **Flip-Flop 1 (FF1)**: Least Significant Bit (LSB)
- **Flip-Flop 2 (FF2)**: Middle Bit
- **Flip-Flop 3 (FF3)**: Most Significant Bit (MSB)

**Connections for T Flip-Flops:**
1. **T Flip-Flop 1 (FF1)**:
   - T input is connected to **logic high** (1), causing it to toggle on every clock pulse.
   - Q output of FF1 is directly connected to the input of FF2.

2. **T Flip-Flop 2 (FF2)**:
   - T input is connected to the Q output of FF1 (T = Q1) through an AND gate.
   - This means FF2 will toggle on every positive edge of FF1's Q when FF1 is high.

3. **T Flip-Flop 3 (FF3)**:
   - T input is connected to the output of an AND gate, which takes inputs from Q1 and Q2. This ensures FF3 toggles only when both Q1 and Q2 are high (when the count reaches 3).

**Circuit Diagram:**

Here is the basic layout for a 3-bit synchronous up counter:

```
        +-----+      +-----+      +-----+
 Clock  |  T  |  Q   |  T  |  Q   |  T  |  Q
 ------>| FF1|---> | FF2|---> | FF3|
        +-----+      +-----+      +-----+
```

- **T input for FF1** is connected to logic high.
- **T input for FF2** is connected to Q output of FF1.
- **T input for FF3** is connected to the output of an AND gate that receives Q1 and Q2 inputs.

### Timing Diagram

To create a timing diagram, follow these steps:

1. **Clock Pulse (CLK):**
   - Represents the clock signal which drives all flip-flops. It toggles at regular intervals.

2. **Q Outputs:**
   - **Q1**: Output of FF1 (LSB), toggles with each clock pulse.
   - **Q2**: Output of FF2 (Middle Bit), toggles when FF1’s Q output is high.
   - **Q3**: Output of FF3 (MSB), toggles when both Q1 and Q2 are high.

**Example Timing Diagram:**

```
Clock:    ______|‾‾|______|‾‾|______|‾‾|______|‾‾|_____
Q1:       ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
Q2:       _____‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
Q3:       _______‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
```

**Explanation:**

- **Clock** pulses at regular intervals.
- **Q1** toggles with each clock pulse.
- **Q2** toggles after Q1 completes a full cycle.
- **Q3** toggles after both Q1 and Q2 complete a full cycle.

### Summary

This 3-bit synchronous up counter counts from 0 to 7 in binary (000 to 111). Each flip-flop toggles based on the outputs of the previous flip-flops, and the timing diagram shows how the outputs change with each clock pulse.