My question involves landlord-tenant law in the State of: California

I am required to give a 30 day written notice of my intention to vacate an apartment? We are currently in a month-to-month agreement due to our original 1 years lease expiring over 2 years ago. I plan to move on September 1st and am wondering if my landlord with have any legal right to demand a 30 day notice, or for me to pay rent until this time next month?

Thank you in advance for your replies!
Gene