Hardware is either 32 bit or 64 bit. The OS is either 32 bit or 64 bit.
While 64 bit hardware can run either a 32 bit or 64 bit OS, 32 bit hardware can only run a 32 bit OS. Most hardware in the last 10 years is 64 bit. A 64 bit OS will not install on a 32 bit system as it will just error out.
Why would you run a 32 bit OS on 64 bit hardware? It's a good option if you intend to run Windows apps under Wine as they require the 32 bit libraries so you'll likely have less problems just by running the 32 bit system.
Last edited by NGIB; 06-23-2014 at 07:39 AM.