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Now here are two questions: The first one is how to ask the question "Did you understand ?" or "Have you understood ?" and the second one is how to answer "I understood" or "I have understood" ?

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"Have you understood?" is very unlikely in US speech, and "Did you understand?" would be used only with reference to some past situation—for instance, "Did you understand what Prof. Sartorius said yesterday?" or "Did you understand what would happen when you pushed that button?"

If what you're interested in is you hearer's current state—whether your hearer understood what was just said—cast it in the simple present:

Do you understand?

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    For contextual reasons, you'd be much more likely to ask Do you understand? rather than Did you understand? in most contexts. You wouldn't normally care if the other person didn't understand something previously - what matters is whether they still need further explanation. Sep 16 '17 at 15:41

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