You cannot install 32 bit program on 64 bit Windows OS. While installing, it will give you an error specifying bit compatibility check. If you are able to install it, it would not work the way it should be.
Wrong. 32 bit apps work under Win 7 x64. Some of the components of 7x64 are still 32 bit, too. Some really old 32 bit apps won't work under Win 7 because of the "Win 7" part, not necessarily the 64 bit part. Or they may have a 16 bit install package, which won't work under 7x64. If you absolutely need to use the app, you might consider running a virtual machine (with something like VMWare, Virtual PC, etc) or installing XP Mode support.