Flooring Tile - 12 X12 Title over old title floor

The old title floor is in good shape (old titles 1 x 1),nothing loose.The floor is off about 1/2 on one side.What is best way of putting new titles on floor.Either rip up old floor or just go over current floor.I have no problem replacing the saddle to match new height of new floor. I am putting in new cabinets,so thats not a problem or is toilet a problem either.

Is this on a concrete slab or a framed floor? If a framed floor, what is the makeup of whats under the tile?

The house is over 30 yrs old and on the second floor.I would say a MUD job,about 1 in thick

Why is the floor off on 1 side by 1/2"? This is the first thing you need to address. When you say its off by 1/2", is there one low spot or are you saying the floor is flat, but its not level - its off by 1/2". Tile doesnt need level, it needs flat, so if its flat and it doesnt bother you, you dont have to make it level.

You can tile over tile. The existing tile should be in good shape, no cracked or loose tile or grout. It needs to be cleaned of wax, grease etc. Rough up the glaze on the surface of the tile with a rough grit sandpaper to make it a better surface for the thinset to bond to. Use a good quality modified thinset when setting the tile.

If I put a 4 ft level by the tub the floor has a high point about 3.5 ft from wall (5X9),thats 5 ft wide.It looks like house has settled or it was done that way.As far as old titles go they aren't cracked, loose and the grout is in good shape. I will sand with course paper and use modified thin set. The thin set will come from HD or Lowes,would they be considered good.

HD carries Custom Building Products thinsets. Lowes carries Mapei and or Laticrete. All good thinsets.