A 32-Bit version of Windows is only capable of addressing 4GB total memory.
This includes the system RAM, GPU memory, BIOS, sound card and all other system devices.
In order to access the full amount of installed memory, you must install a 64-Bit version of Windows.
Unfortunately there is no way to upgrade from 32-Bit to 64-Bit, you must format and reinstall the 64-Bit version.
If you already have a Windows 7 32-Bit license key you do not need to purchase a new license.
You simply need to find 64-Bit install media for the identical version (Home, Professional, Ultimate, etc.) and use your existing key to activate.