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What is the maximum amount of memory supported by a dual core machine?

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Volatile or Non-Volatile Memory?

If it is Volatile, like RAM, then it isn't by the number of cores, but by the number of physical slots available and by processor Bit-Rate. 32 Bit Systems (Processors, Operating Systems, or both) can only access up to 4~ GB of Volatile memory, such as RAM. This is lowered to 3GB, since there is an overhead associated with background operations.
Calculation:
2^32 = 4,294,967,296 bytes
4,294,967,296 / (1,024 x 1,024) = 4,096 MB = 4 Gigabytes if all things are perfect. 64 bit Systems (Processors, Operating Systems, or both) can access a MUCH, MUCH larger well of Volatile memory. Something along the lines of EXAbytes. (Which is two steps beyond Terabyte) 2^64 = 18,446,744,073,709,551,616 bytes
18,446,744,073,709,551,616 / (1,024(Kb) x 1,024(Mb) x 1,024(Gb) x 1,024(Tb)) = 16EB (Exabytes)

Many 64-bit processors have 48-bit addressing, so their actual maximum memory addressing capability is in the Petabyte range.

Non-volatile memory addressing is essentially limitless. I believe there are theoretical limitations, but I don't have the knowledge at hand to calculate them.
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What is the maximum amount of memory any single process on Windows can address and is this different from the maximum virtual memory for the system?

Answer Processes access virtual memory space, not physical memory. Applications never access RAM directly but only through the memory management interface of the processor. D

AMD Dual-Core Processor C60 1.333 GHz with 4 GB DDR3 Memory anyone good... Can you play games on it?

yup! Fear 1, Doom 3 BGF edition, Tomb raiders before the new reboot of 2013, Ps2 and N64 Emulators run pretty smooth, Call of duty MW1 and 2 will run nicely, Portal 2 will be