Ripple Counter and its Working

A ripple counter is a type of digital counter that uses the principle of a ripple carry to increment the count. It is constructed using a series of flip-flops connected in a chain, where the output of one flip-flop serves as the clock input for the next flip-flop in the sequence.

Frequency of Output Signals

In a ripple counter, the frequency of the output signals increases by a factor of two for each successive stage. For example, if the clock input to the first stage of the counter has a frequency of f, then the output of the first stage will have a frequency of f/2, the output of the second stage will have a frequency of f/4, and so on.

Output Periodicity

The output periodicity of a ripple counter is equal to the product of the clock period and the number of counts required to cycle through all possible states of the counter. For example, a 3-bit ripple counter can count from 000 to 111, or a total of 8 states. If the clock period is T, then the output periodicity of the counter will be 8T.

Relation between Output Frequencies and Periodicity

The stage whose output has a frequency equal to 1/8th of the clock signal applied to the first stage is the third stage of the counter. This is because the frequency of the output signals doubles for each successive stage, so the frequency of the third stage output is f/2^3, or f/8.

Since the output periodicity of the counter is equal to the product of the clock period and the number of counts required to cycle through all possible states, we can calculate the output periodicity of the counter as 2^3T, or 8T.

Therefore, the output periodicity of the third stage of the counter, whose output has a frequency of f/8, is also 8T. This is because the output periodicity of each stage of the counter is equal to the output periodicity of the entire counter divided by the number of stages. Since the ripple counter has 3 stages, the output periodicity of each stage is 8T/3, which is equivalent to 8T when rounded to the nearest multiple of the clock period.

Question is wrong , It should be , " ALSO HAS AN INPUT PERIODICITY EQUAL TO 1/8th of output signal , then we can say it is Mod 8 3 bit ripple counter . Answer is 3 bit ripple counter , but this question  really gave me headache when i saw at first . Thing is Input freq is more and output periodicity is more i.e , T out = Tin*8  . And you put this condition you get clear about what question was going to ask but had mis spell Input as output