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The maximum clock frequency in MHz of a 4-stage ripple counter, utilizing flip-flops, with each flip-flop having a propagation delay of 20 ns, is ___________. (round off to one decimal place) 
    Correct answer is between '12.3,12.7'. Can you explain this answer?
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    The maximum clock frequency in MHz of a 4-stage ripple counter, utiliz...
    Given:
    - The ripple counter has 4 stages.
    - Each flip-flop in the counter has a propagation delay of 20 ns.

    To find:
    - The maximum clock frequency in MHz.

    Explanation:
    A ripple counter is a type of digital circuit that counts in binary sequence. In a 4-stage ripple counter, there are four flip-flops connected in series, such that the output of each flip-flop serves as the clock input for the next flip-flop. The output of the last flip-flop is the most significant bit (MSB) of the counter.

    The maximum clock frequency in a ripple counter is limited by the propagation delay of the flip-flops. The propagation delay is the time taken for the output of a flip-flop to respond to a change in the input. In this case, each flip-flop has a propagation delay of 20 ns.

    Calculating the maximum clock frequency:
    The maximum clock frequency can be calculated using the formula:

    Maximum clock frequency = 1 / (2 * propagation delay)

    In this case, the propagation delay is 20 ns, so:

    Maximum clock frequency = 1 / (2 * 20 ns) = 1 / (40 ns) = 25 MHz

    However, it's important to note that the ripple counter has four stages, and each stage introduces an additional propagation delay. Since the outputs of the flip-flops are connected in series, the total propagation delay of the counter is the sum of the individual propagation delays.

    In this case, the total propagation delay is 4 * 20 ns = 80 ns.

    Adjusting for the total propagation delay:
    To calculate the maximum clock frequency, we need to adjust for the total propagation delay of the counter. The adjusted formula becomes:

    Maximum clock frequency = 1 / (2 * total propagation delay)

    Maximum clock frequency = 1 / (2 * 80 ns) = 1 / (160 ns) = 6.25 MHz

    Therefore, the maximum clock frequency of the 4-stage ripple counter, utilizing flip-flops with a propagation delay of 20 ns, is approximately 6.25 MHz.

    Round off:
    Rounding off the answer to one decimal place, the maximum clock frequency is between 6.2 MHz and 6.3 MHz.
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    Community Answer
    The maximum clock frequency in MHz of a 4-stage ripple counter, utiliz...
    Concept:
    For the n-stage ripple counter, the no. of flip-flops used are n.
    If Each flip flop is having propagation delay of tp seconds.
    Then overall propagation delay of the n-stage ripple counter is 'ntp'
    Both of the above diagrams is a 3 stage up counter.
    i.e., 3 flip-flops are used.
    In order to obtain Q2, the 3 clocks will be used at a different instant or at the instant when each flip flop will get their input.
    If each flip flop is having 'tp' as propagation delay, then to get output, the overall propagation Delay will be sum of the propagation Delay of each flip flop.
    Explanation:
    Given
    Ripple counter 4 flip flop 
    tp = 20 n second for each flip flop.
    T = n tp = total propagation delay
    ⇒ T = 4 × 20 n sec = 80 n sec
    Clock frequency = 
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    The maximum clock frequency in MHz of a 4-stage ripple counter, utilizing flip-flops, with each flip-flop having a propagation delay of 20 ns, is ___________. (round off to one decimal place)Correct answer is between '12.3,12.7'. Can you explain this answer?
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