Digital computers calculate by manipulating binary digits

Digital computers calculate by manipulating binary digits (bits; ones and zeroes). Because bits are so simple to handle they can be made easily to stand for almost anything; hence the general usefulness of digital computers. 

  

Bits can symbolize words, instructions, laws of logic or of physics, numerical measurements, recorded images and sounds--anything that can be written down. In using a digital computer to solve a mathematical equation, for example, certain bits inside the computer are arranged to symbolize the constants and variables in the equation and others are arranged to symbolize the mathematical rules for manipulating those constants and variables. When the computer runs, it applies the rules to the variables just as a person would, only faster.

There is another quite different way to solve an equation: instead of symbolizing an equation, one can set up an experiment in which certain physical quantities are analogous to that equation (that is, which behave like it). One sets up a carefully designed experiment, lets it run, and measures some result; this measurement gives the solution of the original equation. Since this kind of computation uses physical events that are analogous to (like) mathematical symbols and rules, it is called analog computing. For example, pouring three equal quantities of water into a tall tube and measuring the height of the resulting column would be an analog method of calculating that x + x + x = 3x.

In one sense all computers are analog computers. Digital computers merely employ more roundabout analogies: in them, voltages are made to behave like binary digits and binary digits are made to behave like higher-level mathematics. Analog computers skip the binary bottleneck, so to speak, and make voltages (or other phenomena) behave like mathematics directly. 

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