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If the processor is 8-core then it isn't x86, it's x64. 

If I'm not mistaken, an x86 processor can't access more than  4GB of memory.

So you can either have 4GB of RAM and an x86 processor, or you can have 8GB of RAM and a x64 processor. 

Also, it's doubtful that it's an AMD-based processor.  If anything, as defined before in the Microsoft literature, it would be a multi-core processor with many different types of processor cores.  That way, you'd have a set of cores dedicated to the game code, and a secondary set reserved for specific functions of the game code or hardware (i.e. Kinect). 

This would allow the core gaming processors to deal with rendering the game, while you may have a dedicated processor for AI, Kinect, etc., ensuring expensive, powerful CPU cores aren't wasted on doing menial tasks that would otherwise waste CPU cycles on.