Existing bathroom is tiled and floor outside is carpet. I want to tile the carpet area and the bathroom with the same tile. I don't want to remove existing tile in the bathroom, just tile on top of it. I planned on removing carpet and installing 5/8 thick concrete board to level the floor with the existing tile, then tile the entire area. How to I attach the concrete board to the concrete floor.

It would seem it would be less expensive to remove the tile from the bathroom and tile everything on the same level.