Giving notice is a courtesy but nothing else. In other words, it is not legally required to be provided to an employer (unless an employment contract or union agreement mandates that it be given). Accordingly, you need not give any notice at all if you so choose. That having been said, if you do decide to give notice, then your employer may or may not honor it. This means that it can accept your notice as immediate, so can take you off of the payroll.