Logical squares

Digital logic implements the functions of boolean algebra. These functions take "true" or "false" as the possible inputs and produce "true" or "false" as output. In the previous pages we saw two examples of functions like these; the inverter and the andgate. There are many other possible functions. Consider, for example, functions of two inputs. Each input can have two possible values so there are four possible input combinations. For each of the possible input combination there are two possible output values, yielding sixteen possible functions. Of these sixteen, a few are names and commonly used. These include and, or, and xor. We have already seen and. Or is the inclusive-or function. Its output is true if either or both of its inputs are true. Xor is the exclusive-or function. Its output is true if either, but not both, of the inputs are true.

From left to right there are structured implementations of the and, or, xor, and invert functions. The loops at the top and the bottom provide test signals. Notice that the inverter uses the same structure as the exclusive or except that one of the inputs is being constantly fed with a one..

If you looked at a modem integrated circuit through a microscope you'd see something that resembled the illustration here. However the analogy can't be taken too literally. While integrated circuity do contain logical functions connected by wires, the operating principles are very different. The logical functions are made up of transistors which switch the voltages that represent the logical values. The wires are made out of metal that is deposited photographically.

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Brian Silverman
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