There is no universal way to decipher that.
If your question is about the Hardware, it ought to have been presented differently.
You could boot into the BIOS and check the specs of the rig if it supports 64Bit computing, that ought to answer the question.

Or else post the specs (ie. Make , model) of the processor and mobo here and we'd tell you if it's 64bit capable of 32bit limited.
Or you could search the same on the internet and get the answer.
 


Actually the OP can use CPU-Z or HWInfo and it usually will indicate a 64 or 32bit system.



You can use either CPU-Z or Speccyhttp://www.piriform.com/speccyhttp://www.piriform.com/speccy to take the guess work out for you.
 
Pls...... He (The OP) has specified in the question itself...... REGARDLESS to the OS.

To the OP.

Read through the Processor Sepcs here:
http://www.cpu-world.com/CPUs/Bulldozer/AMD-FX-Series%20FX-4100.html
Check Data Width and Features.... both specify, 64Bit Tech.

And the Mobo specs here:
http://www.asus.com/Motherboard/M5A78LM_LX/#specifications

And here just check under the Memory section.... if it didn't support the tech, they'd never ask you to install a 64Bit OS to make use of more RAM >4GB.

Although these references are for you, we here out of experience already know that the rig is 64Bit capable.