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First developed in the mid-1800s by mathematician George Boole, Boolean logic is a formal, mathematical approach to decision-making. Instead of the familiar algebra of symbols and numbers, Boole set down an algebra of decision states, such as yes and no, one and zero. The Boolean system remained in academia until the early 1900s, when electrical engineers noticed its usefulness for switching circuits, leading to telephone networks and digital computers.

## Boolean Algebra

• Boolean algebra is a system for combining two-valued decision states and arriving at a two-valued outcome. In place of standard numbers, such as 15.2, Boolean algebra uses binary variables that can have two values, zero and one, which stand in for “false” and “true,” respectively. Instead of arithmetic, it has operations that combine binary variables to yield a binary result. For example, the “AND” operation gives a true result only if both of its arguments, or inputs, are also true. “1 AND 1 = 1,” but “1 AND 0 = 0” in Boolean algebra. The OR operation gives a true result if either argument is true. “1 OR 0 = 1,” and “0 OR 0 = 0” both illustrate the OR operation.

## Digital Circuits

• Boolean algebra benefited electrical designers in the 1930s who worked on telephone switching circuits. Using Boolean algebra, they set a closed switch equal to one, or “true,” and an open switch to be zero, or “false.” The same advantage applies to the digital circuits comprising computers. Here, a high voltage state equals a “true” and a low voltage state equals a “false.” Using high and low voltage states and Boolean logic, engineers developed digital electronic circuits that could solve simple yes-no decision-making problems.

• On its own, Boolean logic gives only definite, black-or-white results. It never produces a “maybe.” This disadvantage limits Boolean algebra to those situations where you can state all the variables in terms of explicit true or false values, and where these values are the only outcome.

## Web Searches

• Web searches use Boolean logic for filtering results. If you do a search on “car dealers,” for example, a search engine will have hundreds of millions of web pages that match. If you add the word “Chicago,” the number drops significantly. The search engine uses Boolean algebra, retrieving pages that match “car” AND “dealer” AND “Chicago;” in other words, the Web page must have all the terms to qualify. You can also specify an “OR” condition, such as “car” and “dealer” AND (“Chicago” OR “Milwaukee”) which gives you pages for car dealers in Chicago or Milwaukee. The advantage of Boolean logic, refining the results of searches, benefits millions who browse the Web every day.

## Difficulty

• The language of Boolean logic is complex, unfamiliar and takes some learning. The “AND” operation, for example, confuses beginners used to its meaning in everyday English. They expect a search for “car” AND “dealer” to give more results than just “car,” as the AND implies adding to results. Boolean logic also requires the use of parentheses to organize a statement’s exact meaning: “car OR boat AND dealer” gives you a list of anything to do with cars added to a list of boat dealers, whereas “(car OR boat) AND dealer” gives a list of car dealers and boat dealers. The disadvantage of Boolean logic’s difficulty limits its users to those that spend the time learning it.

## References

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