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I am curious of what role electrical current plays in a processor. When I asked this back in school a couple years ago, my teacher only replied that the processor executes instructions in response to a series of 0:s and 1:s. However, I cannot grasp how something as seemingly random and unpredictable as an electrical current can be used to execute instructions in a processor that is used for deterministic and predictable operations.

How is electrical current used by a processor?

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Well electrical current isn't random and isn't unpredictable. It's just that in some specific cases a good deterministic model is so complex that people want to do their best not to make it. – AndrejaKo Dec 21 '12 at 23:35
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I'm surprised that you're not equally surprised by a radio. How is it that unpredictable electric current can reproduce sound originating miles away? Clear sound and intelligible speech? – Kaz Dec 22 '12 at 1:37

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Simply put, current is used to charge capacitors to a given voltage. It is then this voltage that is representative of a "1" or a "0". The voltage is the state, the current is the juice that gets you to that state. THis applies to CMOS processors, but since there are few other kinds around this is probably general enough. I'll let the pedants worry about other kinds.

On Edit, I thought I'd mention that the capacitances being charged are the internal gate capacitances of the transistors themselves.

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The processor will do its job by taking the binaries (0's and 1's) in the electrical current to assembly language, and execute the instructions needed.

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This doesn't answer the question, and leaves basically the same question the OP originally asked. Whether assembly or any other language was used to derive the instructions is completely irrelevant. In fact instructions themselves are at a much high level than what is being asked about. – Olin Lathrop Mar 28 at 12:02

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