Hi. My name is***** you for your question and the opportunity to assist. You can run a 32-bit version of Windows on a machine that supports 64-bit processing. I have a machine at home running a 32-bit version of Windows 7 Ultimate on a 64-bit Intel processor.
One thing to keep in mind though is that if the computer you're installing your 32 bit version of Windows on has more the 4GB of RAM, your version of Windows won't recognize it all. That's a limitation of 32 bit operating systems.