The Office 2013 License Thing

Upgraded to Windows 8 in December. I like it, but upgrading from 7 on the same computer seems to have made things slow. I'm considering wiping my HD and installing Windows 8 from scratch. Problem is, I bought Office 2013 right when it first came out through the Home Use Program. It was only $10 so I figured why not. I know you can't install it on a different computer, but can you reinstall it on the SAME computer? And how does Microsoft know it's the same if I've reformatted the hard drive and all that? Thanks tribe. :-)