That sounds like a great IP scheme for you to use. It is simple and relates to the physical layout.
While you will need a router (or a server running router services), you will not need a router for each floor. To insure that the people on eachfloor get the correct IP, there are three ways you can approch the problem:
1) the simple, but possibly more expensive route. Put a server on each floor. If there is already a server on each floor, then just add DHCP to the services aready running. If not, I wouldn't recommend adding an NT or 2000 server. If you are familar with Linux you could add a DHCP server for a very reasonable cost.
2) Also expensive, more initial setup, but less maintainence in the long run and a more elegant solution. Get a router that has a separate interface for each floor or get a multi-homed server that has an ethernet interface for each floor. This is nessary because the DHCP server needs to know where the DHCP request is coming from, physically. A single interface with several IP subnets connected would not be able to distinquish one physical subnet from another.
With that layout you will be able to instruct you server/router to assign IP by interface.
3) You can implement DHCP forwarding agents thoughout your network. this can get complicated, so make sure that you do you homework first.
Good Luck