Boolean Definition

Boolean Definition

Boolean, or boolean logic, is a subset of algebra used for creating true/false statements. Boolean expressions use the operators AND, OR, XOR, and NOT to compare values and return a true or false result. These boolean operators are described in the following four examples:

  • x AND y – returns True if both x and y are true; returns False if either x or y are false.
  • x OR y – returns True if either x or y, or both x and y are true; returns False only if x and y are both false.
  • x XOR y – returns True if only x or y is true; returns False if x and y are both true or both false.
  • NOT x – returns True if x is false (or null); returns False if x is true.

Since computers operate in binary (using only zeros and ones), computer logic can often expressed in boolean terms. For example, a true statement returns a value of 1, while a false statement returns a value of 0. Of course, most calculations require more than a simple true/false statement. Therefore, computer processors perform complex calculations by linking multiple binary (or boolean) statements together. Complex boolean expressions can be expressed as a series of logic gates.

Boolean expressions are also supported by most search engines. When you enter keywords in a search engine, you can refine your search using boolean operators. For example, if you want to look up information about the Apple iMac, but want avoid results about apples (the fruit) you might search for “Apple AND iMac NOT fruit.” This would produce results about iMac computers, while avoiding results with the word “fruit.” While most search engines support boolean operators, their syntax requirements may vary. For example, instead of the words AND and NOT, the operators “+” and “-” may be required. You can look up the correct syntax in the help section of each search engine’s website.

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