Yes. The OS license is tied to the hardware it was installed on not the bit length (32 bit or 64 bit). You should be fine to reinstall with the 64bit code... The main difference between the two is the amount of memory it can handle. 32 bit operating systems will only use up to 3.5GB of memory. With the trend being 4GB or higher in a "standard" build, the 64 bit OS is the way to go. This also trickles down to applications, however there aren't many apps that can utilize (address) more than 3GB of memory.