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Consider the following synchronous counter made up of JK,D,T flip flops as in the image!

now here why J is taken as Q0' (complement) instead of  Q0'' (double complement) you can clearly see a bubble and a q0'  ... as it should be so q0'' right? please clarify!

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Yes, you are right 

it is mod 5 counter

This is my solution tell me if I'm wrong 

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