You can't go from 64-bit to 32-bit without clean install. In other words, installing the 32-bit system over the existing 64-bit and replacing it entirely (=reformat) is necessary. Take backups of files before proceeding. You'll need a full retail copy of Win7 Ultimate x86, and not an "upgrade" disc.
A 64-bit processor will run a 32-bit Windows 7 just fine, but not vice versa.