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?

The number of required bits in our  counter is 9

Explanation:

Given:

Incoming frequency kHz

Output frequency Hz

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

Where number of bits,

Put all required values in above equation,

Take natural log on both side,

    ≅

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