Designing a 3-Bit Counter with J-K Flip-Flops: Counting Up and Down

Recently, I've come across an interesting homework problem that involves designing a 3-bit counter with JK flip-flops. The challenge is to create a counter that first counts up twice and then counts down three times, depending on the input signal. I had done this many years ago, but over time, I had forgotten the specifics. Not to worry, I'll provide a step-by-step guide to tackle this problem. Let's break it down into manageable tasks and explore the concepts in detail.

Task Breakdown

Task 1: Designing a 3-Bit Counter Task 2: Recording the Number of Up-Counts Task 3: Transition from Up-Count to Down-Count Task 4: Recording the Number of Down-Counts

Task 1: Designing a 3-Bit Counter

A 3-bit counter typically uses three JK flip-flops connected in a manner that enables sequential counting. The counter can be either synchronous or asynchronous, but for this problem, a synchronous counter is a good choice to ensure that the transitions between states are uniform and predictable.

How JK Flip-Flops Work

JK flip-flops are edge-triggered devices that can operate in four possible modes: Set (1), Reset (0), Hold (unchanged), and Toggle. The state of the output is determined based on the input values of J and K. For instance, J1 and K0 sets the flip-flop to 1, J0 and K1 resets it to 0, J1 and K1 toggles the state, and J0 and K0 holds the current state.

Task 2: Recording the Number of Up-Counts

To record the number of times the counter completes a full up-count, we need an additional bit of memory. A 4-bit counter can be used to count the number of up-counts. Each time the counter reaches the maximum value (111 in binary, or 7 in decimal), the 4-bit counter increments by one.

For example, if the 4-bit counter is initialized to 0000, it will count up to 1111 (15 in decimal) before it wraps around to 0000. This 4-bit counter will be useful in indicating whether the counter has completed its up-counts and is now ready to start counting down.

Task 3: Transition from Up-Count to Down-Count

Upon reaching the second terminal count-up value (111 in binary), the circuit needs to recognize this and initiate a transition to a down-count. This can be done in a few different ways:

Using a Comparator: A comparator can be used to compare the current value of the 3-bit counter against the desired terminal count (111 in binary). When the comparator indicates that the counter has reached 111, a signal can be generated to switch the counting direction. Using a Set and Reset Logic: Another approach is to use a set and reset logic where the set signal (Set 1) is connected to a state where the counter is allowed to count down, and the reset signal (Reset 1) is used to bring the counter back to the initial value before the next up-count.

For this example, we'll use a set and reset logic. When the counter reaches 111, the set signal to the JK flip-flops will initiate the down-count. This is similar to setting the counter to a predefined start value for the down-count.

Task 4: Recording the Number of Down-Counts

Similar to Task 2, a 4-bit counter can be used to record the number of times the down-count has occurred. Each time the down-count completes, the 4-bit counter increments by one. Once the 4-bit counter has counted down a certain number of times, it will trigger the counter to start counting up again.

For instance, if the 4-bit counter is set to count down 3 times (0011 in binary, which is 3 in decimal), it will increment to 1111 (15 in decimal) and then reset to 0000. At this point, the counter will switch back to the up-count mode.

Conclusion

The homework problem presents an interesting challenge, and by breaking it down into manageable tasks, we can design a 3-bit counter with JK flip-flops that counts up twice and then counts down three times. The key is to use additional bits of memory to record the number of up- and down-counts and to use set and reset logic to control the transition between counting directions. If you have any specific questions or need further assistance, feel free to ask!