We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of flip-flops required to implement this counter is________

According to me, the answer should be 2, as the max. value in the sequence is 3 and 3 can be repeated with 2 bits only.

But my solution manual says the answer should be 4.

I can't really fathom this answer given by my manual.

Am I right? If not why am I getting a wrong answer?

Thanks in advance!

  • 2
    $\begingroup$ Given that the sequence has period 6, you certainly need at least 3 bits of memory. Whether you need more depends on your computation model, which you haven't defined. Assuming that two flip-flops would designate the output, you need at least two more since 0 appears three times in the sequence. $\endgroup$ Mar 3, 2019 at 8:27
  • $\begingroup$ Hi @YuvalFilmus, can you please elaborate about the period thing you talk about in your answer? I find it a little confusing and difficult to grasp. Thank you! $\endgroup$ Mar 3, 2019 at 20:18
  • 1
    $\begingroup$ See Wikipedia: en.wikipedia.org/wiki/Periodic_sequence. $\endgroup$ Mar 3, 2019 at 20:22


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