Mailing the story:

One great thing about Linux is that you can transplant a hard disk from a machine that runs a 32-bit AMD XP processor into a new 64-bit Intel Core 2 machine, and the Linux installation will continue to work. However, if you do this, you'll be running a 32-bit kernel, a C library, and a complete system install on a processor that could happily run 64-bit code. You'll waste even more resources if your new machine has 4GB or more of system memory, and you'll be forced to either not use some of it or run a 32-bit Physical Address Extension (PAE) kernel. Cross-grading to the 64-bit variant of your Linux distribution can help you use your resources more wisely.