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Intel and AMD's dual-core technology doesn't run as two separate CPUs, like the old dual-processor machines of old. They run in concert and have their functioning in concert managed by an on-chip controller.
The net effect is that although you are getting the benefit of a dual-processor machine, you're pumping bits into it as though it were one processor.
That said, you can't realize the benefit of a dual-core chip without having an application that can multithread. If your application runs as a single thread, then only one processor can handle it; if you can run it as two or more threads, the controller can hand off the work to either core, depending on the workload of each thread and core.
However, if you continue writing your code as you have, you'll see no difference in execution (except, of course, that even in dual-core CPUs, the individual cores continue to get better and faster with each new chip, so newer processor generally equals faster, better execution of the same code).
http://en.wikipedia.org/wiki/Dual_core
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