Real World Examples #5 – Clock Divider by 5

August 26, 2009

Here is a neat little circuit that was used in an actual project a long, long time ago (in a galaxy far, far away…).

The requirement was to build a divide by 5 circuit for the clock with 50% duty cycle. The initial (on reset) behavior was not important – i.e. the circuit could wake up in an undefined state, but should have settled after a given time. The engineer produced the circuit below:


Basically, the circuit is made out of a 3-bit counter, that counts from 000 to 100 and then resets. Signal ‘X’ goes high when the value of the counter is either 000, 001 or 010. Signal ‘Y’ goes high when the counter equals its ‘middle’ state 010. ‘Z’ is a sample on the falling edge of ‘Y’ in order to generate the 50% duty cycle.

So far so good. The general thinking was OK, but there was a major problem with the circuit, can you discover what it was? How would you fix it in RTL? and more important, how would you fix it in an ECO (as it was eventually done)?

No extra flops are allowed!


  1. Glitches on X. Insert posedge flops in X and Y.

  2. imagine there are no flops available for the ECO.
    anyways a flop in Y is NOT necessary

    • Prior to imagining a world with no ECO flops, inserting a flop on X and not Y would have created a half-cycle “glitch” after Z deasserted.
      Sans flops…
      Connect X to count[2] through inverter. OR in another compare to the Y condition when count==011. X becomes extended by one cycle, but so does Y (and Z) and X is glitch-free.

      • If flop is allowed, insert a flop on the final output.2 flops are not necessary.

    • Jumped the gun… You can avoid the inverter by changing the final AND to an OR (or NOR) and changing the sense of both inputs. Then you can avoid the extra comparator by connecting Y to count[1].

    • Sheesh, is it time to go home already?! 🙂
      Change the AND to OR and just remove the one input bubble. Or… leave it as AND, but add a bubble to X input – whichever is smaller/easier/possible.
      So… X=count[2], Y=count[1], clkout=X||Z or clkout=!X&&!Z.
      And if it changes after this… I give up!

    • Remove both the clouds that generate X and Y. Use bit 1 of the counter (00110) as X. Register X on the falling edge to generate Z. Then OR them to get the clock out.


      • Take count[1] as X and Y.
        Place a Mux between X and Y for the output.
        Use count[2] as the select line.

        i.e output = Y when count[2]
        output = X when !count[2]

      • In My comment I did a mistake.. The Mux is between X and Z..

  3. How about to change the counter to a Johnson counter (000, 100, 110, 111, 011, 001)!
    If the counter is done to count from 000 to 011 we can test only the last bit (==0) to generate the X value and the second bit (==1)to generate the Y value.

    • I made some changes on my proposal, duty cycle was not 50% – 50%…

      Seems to work right now!!!

    • Johnson counters (which is a form of gray counting) is the way to go when doing clock dividers. (actually normal Gray counters should also be OK)

  4. In case the flop has an unused (asynchronous) reset input:
    X = 1
    Y <= Z or (=001)
    reset <= (MSB of count = 1)

    that might work since (MSB of count = 1) should be glitch-free
    and the sequence 100-000-001 is also free of potential glitches…


  5. May be we can replace Z by
    Z(n)= Y + (X * Z(n-1)).
    Assuming than Z is zero initially (resetted),
    for 000,001 Z=0, thus making OUT=X=1.
    For 010, when Y goes to 1, Z will go to 1, thus making
    output 0.
    For 011, if X becomes 0 before the negedge, then output will be zero. If it is still 1 at negedge, Z(n-1) combined with X will still keep Z at 1, thus keeping out at 0.


  6. Clock dividers by 3 and 5 lead to the following question: what’s the simplest circuit that divides a clock by any odd number with 50% duty cycle.

  7. Recycle counter as D0, D1, D2.

    always @(posedge clk)
    D0 <= ~(D1 | D2);
    D1 <= D0;
    D2 <= D1;

    always @(negedge clk)
    D3 <= D2;

    clk_out = ~(D3 | D2);

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    to see such a nice list. It definitely help out to million, i guess.

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  10. So which of these answers is the correct one:
    a) X==(000|001|100), Y==(001)
    b) X==(000|001|010|011), Y==(010|011)
    c) X==(001|010|011), Y==(000)
    d) Both a) and c) are correct!

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  13. Logically, I am not seeing any error in the above circuit.
    Can you pls point me out the error??

    How about generating x == ! (cnt[0] || cnt[1], and then connect x to the input of negedge triggered flop and output is finally (x or z);

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