Boolean expression

In computer science, a Boolean expression is an expression in a programming language that produces a Boolean value when evaluated, i.e. one of true or false. A Boolean expression may be composed of a combination of the Boolean constants true or false, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions.^[1]

Boolean expressions correspond to propositional formulas in logic and are a special case of Boolean circuits.^[2]

Boolean operators

Most programming languages have the Boolean operators OR, AND and not; in C and some newer languages, these are represented by "||" (double pipe character), "&&" (double ampersand) and "!" (exclamation point) respectively, while the corresponding bitwise operations are represented by "|", "&" and "~" (tilde).^[3] In the mathematical literature the symbols used are often "+" (plus), "·" (dot) and overbar, or "∨" (cup), "∧" (cap) and "¬" or "′" (prime).

Examples

• The expression "5 > 3" is evaluated as true.
• The expression "3 > 5" is evaluated as false.
• "5>=3" and "3<=5" are equivalent Boolean expressions, both of which are evaluated as true.
• Of course, most Boolean expressions will contain at least one variable (X > 3), and often more (X > Y).

See also

• Expression (computer science)
• Expression (mathematics)

References

1. Gries, David; Schneider, Fred B. (1993), "Chapter 2. Boolean Expressions", A Logical Approach to Discrete Math, Monographs in Computer Science, Springer, p. 25ff, ISBN 9780387941158.
2. van Melkebeek, Dieter (2000), Randomness and Completeness in Computational Complexity, Lecture Notes in Computer Science 1950, Springer, p. 22, ISBN 9783540414926.
3. E.g. for Java see Brogden, William B.; Green, Marcus (2003), Java 2 Programmer, Que Publishing, p. 45, ISBN 9780789728616.

External links

• The Calculus of Logic, by George Boole, Cambridge and Dublin Mathematical Journal Vol. III (1848), pp. 183–98.