Final answer:
A mod 5 synchronous up counter using J-K flip-flops requires at least three flip-flops, where the J and K inputs are configured based on a state table to cycle through five states and then reset. Logical gates are also incorporated to manage the reset from '4' to '0'.
Step-by-step explanation:
The design of a mod 5 synchronous up counter using J-K flip-flops involves configuring the flip-flops such that they follow a sequence of five states (from 0 to 4) and then reset to 0, repeating this cycle continuously. Each flip-flop in the counter represents one bit of the binary count. In a mod 5 counter, we need at least three flip-flops to represent counts from 0002 (010) to 1002 (410), since the 5th state (1012, which is 510) is not used.
To design this counter, we start by creating a state table and then determine the JK inputs for each state transition. Set up the flip-flops so that each J-K input will cause the necessary toggling. For a synchronous counter, all flip-flops are driven by the same clock pulse and will change state together on the clock's rising edge. Here is a simplified guide to the JK inputs:
- J and K inputs are both 1 if the flip-flop should toggle.
- J and K inputs are both 0 if the flip-flop should stay in its current state.
- The last flip-flop's J and K inputs will be connected to the AND gate outputs, which are in turn connected to the outputs of the previous flip-flops, to detect the count of '4' and reset the counter to 0.
The complete design will include the flip-flops connected in series, with the output of each driving the JK inputs of the next, according to the state diagram derived from the state table. Additional logical gates (like AND gates) are required for the reset logic to ensure the counter goes from '4' back to '0'.