Logical Operators

Module by: Don Johnson

Summary: A very short overview of logical operators, and how they relate to binary addition.

Note that the logical operations of AND and OR are equivalent to binary addition (if carries are ignored). When used, logical operators indicate truth or falsehood. For example, the statement A∧B A B , which represents "A AND B", will be true if both A is true and B is true, and false otherwise. You could use this kind of statement to tell a search engine that you want to restrict hits to cases where A and B occur together, and not other cases. The statement A∨B A B represents "A OR B". It will be true if A is true, or B is true, or both, and false if A and B are both false. Note that if we represent truth by a "1" and falsehood by a "0", binary multiplication corresponds to AND statements, and binary addition corresponds to OR. The Irish mathematician George Boole discovered this equivalence in the mid-nineteenth century. It laid the foundation for what we now call Boolean algebra, which expresses logical statements as equations. More importantly, any computer using base-2 representations and arithmetic can also easily evaluate logical statements. This fact makes an integer-based computational device much more powerful than might be immediately obvious.

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This work is licensed by Don Johnson under a Creative Commons Attribution License (CC-BY 1.0).

Last edited by Elizabeth Gregory on Aug 10, 2004 8:54 am GMT-5.