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Homework Help: How to know the duty-cycle of a counter

  1. Jan 11, 2017 #1
    1. The problem statement, all variables and given/known data
    Consider the following circuit of a counter with a clock signal of 84 kHz

    As we can see the counter counts down. Show all the states and transitions of this counter and identify all the states using a binary representation. Calculate the frequency and the duty-cycle of the signal labeled 2

    2. Relevant equations
    3. The attempt at a solution

    So I didn't have any trouble with the first part of the problem, The states should be 1100 - 1011 - 1010 - 1001 - 1000 - 0111 and it repeats (so a total of 6 transitions).
    Now the second part is the one that I'm not sure if I'm thinking correctly because this question never appeared to me.

    My attempt to calculate the frequency. If I have 6 transitions all I have to do is to divide the clock frequency by the number of transitions (because If I had the period I would multiply it by the number of transitions). Anyway, I did it and obtained 14 kHz. Now the duty-cycle... I know what a duty-cycle. It's the percentage in the clock transition where the signal is high right? So it should be 1/6 = 17%....

    I have no idea if I'm doing this correctly... I have a good feeling about the frequency but have no idea about the duty-cycle. Can someone give me some help? Thanks!

    EDIT: The sequence is now correct
    Last edited: Jan 11, 2017
  2. jcsd
  3. Jan 11, 2017 #2


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    Perhaps I'm a bit rusty but I'm struggling to understand this bit..

    Shouldn't the sequence go..
    then repeat?

    As for the duty cycle.. Try plotting the wave forms for the clock and node 2 on squared paper or similar.
  4. Jan 11, 2017 #3
    Yes, sorry I misread the last one.

    Is the frequency correct?

    Also for the duty cycle, I'm not getting it I'm sorry, can you be more explicit please?
  5. Jan 11, 2017 #4


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    Yes the frequency is 14KHz.

    Well start by drawing the clock waveform. Then below it draw the waveform for the 4 outputs of the counter. On the first clock edge assume it's loaded with 1100. Then on the next clock edge they become 1011 etc

    I would continue plotting for a bit more than one repeat (eg draw the wave forms for 8 to 10 clock cycles.

    PS I haven't actually checked that the counter is counting down.
  6. Jan 11, 2017 #5
    Thanks. So I did what you told me and obtained (naming the signal Q3Q2Q1Q0)

    Q0: 010101 010101 010101 010101 010101...
    Q1: 011001 011001 011001 011001 011001...
    Q2: 100001 100001 100001 100001 100001...
    Q3: 111110 111110 111110 111110 111110...
    Now the duty-cycle should be 2/6 = 33%? Because for each signal cycle we have 2 ones and 4 zeros...
    Last edited: Jan 11, 2017
  7. Jan 11, 2017 #6


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    Yes that's what I make it.
  8. Jan 11, 2017 #7
    Nice! Thank you very much for the help!
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