I do Know or I did knew?
How can I use this way to say "Yes, I do"?

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Answer

"Yes, I do know that."  "Yes, I did know that." ("Did knew" is an impossible combination: only one past tense per statement allowed.)

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yes, i know. yes, i knew.

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PRESENT: I know (now) his name.

PAST (some): The minute I saw him I knew (past) his name. 
I knew his name at the time but I don't know it now.
I did know (past) his name once upon a time.  - maybe I have since forgotten