It depends on your processor model configuration.
Download the Intel Processor Identification Utility from intel website. Identify your processor model using the utility and then find the specifications of your CPU on intel website and check if the "Intel® 64 Architecture" is supported for your CPU. If it is supported then you can install x64 OS.
For example, my Xi 3650 has Intel Core 2 Duo P8400 2.26GHz (1066 System Bus) and supports x64 architecture. http://ark.intel.com/cpu.aspx?groupId=35569