Sec 6.2 - 188 The Silicon Web: Physics for the Internet Age...

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188 The Silicon Web: Physics for the Internet Age to some well-def ned instructions. Such a process is called logic . It is similar to the human activity oF reasoning. A simple example occurs in a calculator when you press the “add” or “ + ” button. The input data are the two numbers you want to add (18, 5). The calculator carries out several logical operations to produce the resulting sum (18 + 5 = 23), which is the output data. BeFore we consider the actual electronic circuits that perForm the operations, we will discuss the principles behind logic. English mathematician George Boole (1815–1864) was one oF the Founders oF the principles oF logic. In his honor, the methods used are called Boolean logic . In the context oF modern computing, Claude Shannon was the most in± uential scientist who contributed to the theory oF logic. In 1938, as a graduate student at Massachusetts Institute oF Technology, he submitted his master’s thesis that showed how electronic circuits could be used to perForm logic. Ten years later Shannon published the paper, “A Mathematical Theory oF Communication,” which revolutionized scientists’ under- standing oF the concept oF inFormation. 6.2 CONCEPTS OF LOGIC What is logic? In everyday liFe, it means to take in some inFormation, apply certain rules oF reasoning, and produce a decision. ²or example, you might reason that “iF the sky is blue then I will take a walk without an umbrella, but iF the sky is cloudy then I will take my umbrella.” The color oF the sky is the input data and the umbrella decision is the output data. We can make a table showing our logic about the sky and umbrellas: Input: Sky blue? Output: Umbrella? No Yes Yes No The rules we use to process data or inFormation are called logic operations . A logic operation is an elementary rule For arriving at a logical outcome. Three basic opera- tions that can serve as building blocks For all logic operations are NOT, AND, and OR. In considering complex situations, a diagram is useFul to help visualize the logic process. Think oF this as a ± ow chart For making a decision. IF you Face a complicated decision, such as which college to attend, there might be many Factors to consider. Let us say that college B is a better school academically. Your rules For making a decision are: IF college B oFFers you a scholarship, or iF college B’s dorms have DSL lines (high-speed Internet connections), then you would attend B. However, iF college A oFFers you a schol- arship, but not college B, and iF college B’s dorms do not have DSL, then you would attend A. IF neither A nor B oFFers a scholarship or DSL, then you would choose neither. A ± ow chart For this decision is shown below in Figure 6.1 . The particular case illus- trated is indicated by the circled data.
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Sec 6.2 - 188 The Silicon Web: Physics for the Internet Age...

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