Consider the use of a counter to divide an incoming clock. If our incoming clock signal is 32.768 kHz and we need a 64 Hz signal, how many b

Question

Consider the use of a counter to divide an incoming clock. If our incoming clock signal is 32.768 kHz and we need a 64 Hz signal, how many bits would our counter need to have (i.e. what is n) to divide the incoming clock correctly?

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Euphemia 2 months 2021-07-28T10:49:26+00:00 1 Answers 4 views 0

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    2021-07-28T10:51:02+00:00

    Answer:

    The number of required bits in our  counter is 9

    Explanation:

    Given:

    Incoming frequency f_{1} = 32.768 kHz

    Output frequency f_{2} = 64 Hz

    From the formula of finding the number of required bits of a counter,

      f_{2} = \frac{f_{1} }{2^{n} }

    Where n = number of bits,

    Put all required values in above equation,

       64 = \frac{32768}{2^{n} }

       2^{n} = \frac{32768}{64}

       2^{n} = 512

    Take natural log on both side,

     2 \ln n= \ln (512)

      n \times 0.693 = 6.2383

      n = \frac{6.2383}{0.693}

       n9

    Therefore, the number of required bits in our  counter is 9

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