Most of the Dual core processor support 64 bit architecture so it can install both 32 and 64 bit OS

also the main difference between 32bit os and 64 bit os is that 64-bit version of Windows can use more memory—4 GB (gigabytes) or more—and a 32-bit version of Windows is limited to about 3.5 GB or less Ram.
here is an excerpt from microsoft
Computers with a 64-bit processor can run either a 32-bit or 64-bit version of Windows just fine. So it doesn’t matter too much which version of Windows you install on most PCs with a 64-bit processor—unless you want to be able to use more than 3.5 GB of memory.
http://windows.microsoft.com/en-US/w...64-bit-windows