"Have to" is used to express obligation.
- I have to add new material to this site.
"Don't have to" does not express negative obligation or prohibition. It means that there is no obligation. The action is not necessary, not required.
- If you have your boarding pass you don't have to check in at the terminal.
"Got" is often used with "have to" in the contracted form.
- We've got to go over the sales figures before the meeting.
"Got to" can be pronounced "gotta".
- She's gotta buy a new dress for the wedding.
In the first person singular it's not uncommon to hear someone say:
- I gotta go.
- I have got to go.
- I've got to go.