I have the following realisation:

enter image description here

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?

  • \$\begingroup\$ Do you know what a permutation group is? \$\endgroup\$
    – DonFusili
    Dec 18, 2019 at 9:10
  • \$\begingroup\$ No, I haven't heard that term before. Although it sounds like something belonging to group-theory? \$\endgroup\$
    – Carl
    Dec 18, 2019 at 9:11
  • 1
    \$\begingroup\$ 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. \$\endgroup\$
    – DonFusili
    Dec 18, 2019 at 9:13
  • \$\begingroup\$ Is that really the only way to do this? It seems like a very advanced method. \$\endgroup\$
    – Carl
    Dec 18, 2019 at 9:15
  • 1
    \$\begingroup\$ 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. \$\endgroup\$
    – DonFusili
    Dec 18, 2019 at 9:16


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