Windows 7 32 bit



Not exactly.
Windows 7 32 bit will run just fine on a pc with more ram, you just can't access more than about 3.5gb of it.
 
Well, Windows 32-Bit can address the full 4GB, but that includes all devices attached to the system (RAM, GPU, BIOS, sound card, addon boards, network controllers, etc.).
What Win-32 can address from the RAM will be a little less than 4GB less the amount of RAM on your GPU.
If you would like to have access to all the installed memory, you would need to install a 64-Bit OS.