Designing a 3-Bit Synchronous Counter Using J-K Flip-Flops for Custom Sequencing

Designing a synchronous counter with custom counting sequences using J-K flip-flops can be a challenging task, but it is also a fascinating exercise in digital logic design. In this article, we will walk you through the process of designing a 3-bit synchronous counter that follows a specific counting sequence based on input conditions. This counter will have the following sequences:

Understanding the Requirements

When the input is 0, the counter should count as follows: 2 (010) → 4 (100) → 5 (101) and repeat. When the input is 1, the counter should count as follows: 5 (101) → 1 (001) → 2 (010) and repeat.

State Transition Table

To design the counter, we first need to create a state transition table. This table outlines the next state of the counter based on the current state and the input.

Current State Q2 Q1 Q0 Next State Q2 Q1 Q0 Decimal n 010 100 2 → 4 100 101 4 → 5 101 010 5 → 2 101 001 5 → 1 001 010 1 → 2 010 101 2 → 5

Determining J-K Flip-Flop Input Conditions

Next, we derive the J and K inputs for each flip-flop based on the state transitions. The J-K flip-flop behavior is as follows:

J 1, K 0: Set Q goes to 1 J 0, K 1: Reset Q goes to 0 J 1, K 1: Toggle Q changes state J 0, K 0: No change

Input 0

For transitioning from state 2 (010) to state 4 (100):

Q2: J1, K0 (Set) Q1: J0, K1 (Reset) Q0: J0, K0 (No change)

Input 1

For transitioning from state 5 (101) to state 1 (001):

Q2: J0, K1 (Reset) Q1: J0, K1 (Reset) Q0: J1, K0 (Set)

J-K Input Expressions

Based on the current states and the input, we can derive the J and K inputs for each flip-flop:

Q2 (Most Significant Bit)

For Input 0: J2 Input (Q1 Q0), K2 Input (Q2 Q0)

Q1 (Middle Bit)

For Input 0: J1 Input (Q2 Q0), K1 Input (Q1 Q2)

Q0 (Least Significant Bit)

For Input 0: J0 Input (Q1 Q2), K0 Input (Q0 Q1)

For transitioning from state 5 (101) to state 1 (001):

Q0 (Most Significant Bit)

For Input 1: J2 Input (Q1 Q0), K2 Input (Q2 Q0)

Q1 (Middle Bit)

For Input 1: J1 Input (Q2 Q0), K1 Input (Q1 Q2)

Q0 (Least Significant Bit)

For Input 1: J0 Input (Q1 Q2), K0 Input (Q0 Q1)

Circuit Implementation

Finally, we implement the J-K flip-flops with the derived J and K inputs:

Connecting J-K Flip-Flops

Connect the J and K inputs to the corresponding logic expressions derived above.

Common Clock Signal

Connect all flip-flops to a common clock signal for synchronization.

Reset Mechanism

Implement a reset mechanism to initialize the counter at a known state.

Simulation and Testing

Once the circuit is designed, simulate it using a digital logic simulator to verify that it behaves as expected for both input conditions. This ensures the counter follows the specified sequences and operates correctly.

This design allows you to implement a 3-bit synchronous counter with J-K flip-flops that follows the specified sequences based on the input condition.