Flooring Tile - Subfloor trouble

I had an addition built onto the kitchen this past spring and I am finally getting ready to lay the floor. The contractor did a good job of lining up the new floor to the existing but there is still a slight mismatch in places. It is mostly from the old floor. In some places it is higher and in some places it is lower by about an 1/8". The addition has 3/4" t&G plywood while the old floor has 3/4 X 6" T&G. Both have 10" joyce X 16" centers spanned 12". The old floors boards are 50+ years old and have separated in places + a few have cupped a little.

My question is what do I have to do to make this setup good for Ceramic tile? I plan on using cement board. Is there anything I can do to the floor before I lay the cement board?

Thanks

OK, upon further research I see I can't put the cement backerboard overtop of wood planks. It has to be over plywood. My question now is what would be the min thickness of plywood I could get away with since I only have 7/8" before I reach the adjoining rooms floor?

1/2" backerboard + 3/8" tile = trouble?

thanks

Cover both areas of the floor with 3/8 plywood, 1/4 cement board over thinset, and then tile. It may be 1.8 or so higher, but the ceramic installation will last. Ceramic is too expensive to take unnecessary chances with to match the surrounding floors exactly. Close to the right height will be ok.

Shoot, I already bought 15 sheets of the 1/2". Can I get away with another 1/4" higher? My son will kill me if I tell him we have to take it all back. :(

Go ahead with the 1/2 instead of the 1/4 cement board, but use no less than 3/8 plywood.

OK, thanks. :)