For a Windows user you can check the processor type using the following way :
- Right click My Computer and choose Properties.
- Click the Advanced tab.
- Click Environment Variables.
- In the System variables find a variable with the name PROCESSOR_ARCHITECTURE. If your PC has a 32-bit processor, this variable will have a value of x86. If it has a 64-bit processor this variable will have a value of x64.
This way is not a real world test for checking the processor type because those variables can be changed by anyone but at least you can use this way.
To check the processor type for another machine or another operating system you can use this link http://support.esri.com/index.cfm?fa=knowledgebase.techarticles.articleShow&d=31892 as a reference.