# Determine maximum length of repetitive sequence in synchronous FSM

I have the following realisation:

The figure shows a synchronous circuit with the clock on Rising Edge. The circuit will generate a sequence of values on the output (abcde) of the five D-flip-flops. For $$\t=0\$$ the output abcde = $$\"10000"\$$.

I am asked to determine the length of the maximum repetitive sequence of the circuit, but I don't know how to.

I have the answer to this question, and it turns out that the longest sequence has a length of 16. But there is no explanation of how you arrive at this answer. Can someone clarify how the procedure is done?

• Do you know what a permutation group is? Dec 18, 2019 at 9:10
• No, I haven't heard that term before. Although it sounds like something belonging to group-theory?
– Carl
Dec 18, 2019 at 9:11
• Yeah, your circuit basically implements a simplified version of a CRC calculator (simplified as in the input is constant), so you can find the CRC polynomial and calculate the cycle length of the corresponding permutation group. Dec 18, 2019 at 9:13
• Is that really the only way to do this? It seems like a very advanced method.
– Carl
Dec 18, 2019 at 9:15
• No idea, it's the way I would do it, but my guess would be that the constant input would give a simpler procedure, which is why I only commented instead of answered, so it can just be deleted when someone gives you the easy solution. Dec 18, 2019 at 9:16