Final answer:
To design the specified MOD-5 counter with a counting sequence of 0, 1, 2, 4, 6 using JK flip-flops, we must first calculate the number of flip-flops needed, create a state table, derive JK input logic, construct a logic diagram that includes self-correcting feedback, and finally verify the counter's correct operation.
Step-by-step explanation:
Designing a MOD-5 Counter with JK Flip-Flops
To design a MOD-5 counter that counts in the sequence 0, 1, 2, 4, 6 using JK flip-flops, we start by considering the number of flip-flops required. Since it's a MOD-5 counter, it will have 5 states, and we need three flip-flops to represent states from 0 to 7 (2³ = 8, which is the nearest power of 2 greater than 5).
Next, we need to create a state table that includes the present state and the next state, as well as the corresponding JK inputs for each flip-flop that will achieve the desired count sequence. Considering the unused states as don't care conditions, we can fill the table with entries that facilitate easy transitions between the used states.
After deriving the JK inputs from the state table, we proceed to draw a logic diagram that connects the JK inputs to the outputs of the flip-flops based on the logic we've determined. It's essential to include feedback from the output to the input of the flip-flops to ensure that the counter is self-correcting. This means if the counter somehow enters an unused state, it will automatically return to the correct count sequence on the next clock pulse.
Finally, we should verify the design by simulating the sequence or by carefully checking the logic to make sure that, regardless of the starting state, the counter will always follow the desired sequence 0, 1, 2, 4, 6, and then recycle back to 0.