Can I run 64-bit VM guests on a 32-bit host?

If I have a physical PC with 32 bit can I launch a VM that is 64 bit?
What virtual machine software (Virtual PC or VirtualBox or other) would allow this?

I read out there that VMware may support this but I am looking for something Open source or free.

Host would preferably be a Windows host but could be Linux. Guest needs to be Windows.

Thanks


Question: Why did Dumbledore never ask Harry how to destroy a horcrux?
Answer: Why would he need to ask Harry when Harry had already told him how he destroyed the diary?  Dumbledore being Dumbledore was the only one (that we know of) that realized that the diary was a horcrux in the first place.  I doubt that he would need further explanation after Harry told him that he stabbed the book with a fang and the ink came out and it sounded like it was dying...