Digital or binary logic has fascinated many people over the years. The very idea that a two-valued number system can possibly be the basis for the most powerful and sophisticated computers seems astounding, to say the least. Nevertheless, it is so, and the how and the why of this requires some explanation.
Everything in the digital world is based on the binary number system. Numerically, this involves only two symbols: 0 and 1. Logically, we can use these symbols or we can equate them with others according to the needs of the moment. Thus, when dealing with digital logic, we can specify that:
0 = false = no
1 = true = yes
Using this two-valued logic system, every statement or condition must be either "true" or "false;" it cannot be partly true and partly false. While this approach may seem limited, it actually works quite nicely, and can be expanded to express very complex relationships and interactions among any number of individual conditions.
One essential reason for basing logical operations on the binary number system is that it is easy to design simple, stable electronic circuits that can switch back and forth between two clearly-defined states, with no ambiguity attached. It is also readily possible to design and build circuits that will remain indefinitely in one state unless and until they are deliberately switched to the other state. This makes it possible to construct a machine (the computer) which can remember sequences of events and adjust its behavior accordingly.
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