Have = perfect tense Did = past tense

One is simple past tense (didn't), and the other present perfect (haven't). Present perfect tense describes ongoing activities that have continued to the present time or something that happened at some unknown time in the past. Does adding the negative change anything? Not really.

Use "didn't" when you want to talk about an action that happened and finished in the past. For example: suppose there was a live football game on television last night.The following day which is today a friend asks you "Did you watch the game last night?" You say "No, I didn't" Use "haven't" for actions that happened in the past but still continues at the time of speaking. For instance: A friend gave you book yesterday.You start reading it.And you read just one chapter then you put the book away.Today your friend asks "Have you finished that book?" you say "No, I haven't" In this case, you read one chapter not the whole book you may finish the book in the future but at the time of speaking you've only read one chapter.

I haven't got your book I didn't get your book ( It is short for ) I have not got your book. I did not get your book

'haven't' and 'didn't' are used only as auxiliaries. You need to study the past tense and the present perfect tense. You can find that in any course book.