For a 32-bit version operating system:

Microsoft Windows XP Professional Version appears under System
For a 64-bit version operating system:
Microsoft Windows XP Professional x64 Edition Version appears under System.

Method 2

• Click Start-->Run.
  
• Type msinfo32.exe and hit press Enter.
  

Under "System Information", review the value for the System Type item:

For 32-bit editions of Windows XP, the value of the System Type item is x86-based PC.
For 64-bit editions of Windows XP, the value of the System Type item is x64-based PC.