Depends what you mean by a "32-bit host".  If you mean hardware with a 32-bit processor that doesn't have 64-bit capabilities, then no, you can't do that through virtualisation - you would need an emulator rather than virtualisation and I'm not aware of one existing.

If you mean on a machine with a 32-bit OS, then again, it's not possible to run a 64-bit guest on a 32-bit OS without emulation (something would need to translate the 64-bit instructions into 32-bit instructions) unless either (a) the 32-bit OS allows 64-bit applications (like Mac OS X) or (b) you can bypass the OS with a hypervisor.  I'm not aware of a 32-bit type II virtualisation product for the Mac that allows a 64-bit OS to run as a 64-bit app.  In fact, I'm not aware of a type II virtualisation product for the Mac at all.

If you're using a hypervisor (type I virtualisation) like Hyper-V, VMWare ESX, Virtual Box, etc, then it should be possible, because the guest OS does not run on the host OS, but on the hypervisor.  Indeed, the "host" OS actually runs on the hypervisor too.

Can I run 64-bit VM guests on a 32-bit host?
Is there a rule which determines whether it allowable for a word to be "merged" with "all" to make a new word starting "al-"

e.g.


  1)All together -> Altogether
  
  2)All right -> Alright


The first is generally accepted. Whereas I believe the second is technically not (certainly my English teacher used to condemn it).
