Calculators store numbers in binary – 1’s and 0’s. To do something like addition, these 1’s and 0’s are compared two at a time. Each comparison takes roughly the time it takes for electricity to flow one millimeter or less. Electricity travels near the speed of light. You can do several of these comparisons at a time. The result is that millions or even billions of tiny comparisons can happen in less than 100 milliseconds (roughly the time it takes for a human to notice delay). Depending on the hardware, as few as two such comparisons are necessary for every binary digit. As such, adding two numbers which are each less than 65,535 can take only 16 comparisons.
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