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No . YOu don't need to take hold time into consideration while calculating the max frequency of a circuiit . The easiest way to solve hold time violations is to add delay in the data path. So hold time is not necessary
As I said before fixing hold time is a relatively simple job of adding delay buffers in the data path. The reson that it is not considered during intial design of circuit is because you would like to wait until all the steps are over before adding delay buffers.
Would a circuit work if it violates hold time ? NO
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