Boolean data type

In computer science, the Boolean data type is a data type that has one of two possible values (usually denoted true and false), intended to represent the two truth values of logic and Boolean algebra. It is named after George Boole, who first defined an algebraic system of logic in the mid 19th century. The Boolean data type is primarily associated with conditional statements, which allow different actions by changing control flow depending on whether a programmer-specified Boolean condition evaluates to true or false. It is a special case of a more general logical data type (see probabilistic logic)—logic doesn't always need to be Boolean. In computer science, the Boolean data type is a data type that has one of two possible values (usually denoted true and false), intended to represent the two truth values of logic and Boolean algebra. It is named after George Boole, who first defined an algebraic system of logic in the mid 19th century. The Boolean data type is primarily associated with conditional statements, which allow different actions by changing control flow depending on whether a programmer-specified Boolean condition evaluates to true or false. It is a special case of a more general logical data type (see probabilistic logic)—logic doesn't always need to be Boolean. In programming languages with a built-in Boolean data type, such as Pascal and Java, the comparison operators such as > and ≠ are usually defined to return a Boolean value. Conditional and iterative commands may be defined to test Boolean-valued expressions. Languages with no explicit Boolean data type, like C90 and Lisp, may still represent truth values by some other data type. Common Lisp uses an empty list for false, and any other value for true. The C programming language uses an integer type, where relational expressions like i > j and logical expressions connected by && and || are defined to have value 1 if true and 0 if false, whereas the test parts of if, while, for, etc., treat any non-zero value as true. Indeed, a Boolean variable may be regarded (and implemented) as a numerical variable with one binary digit (bit), which can store only two values. The implementation of Booleans in computers are most likely represented as a full word, rather than a bit; this is usually due to the ways computers transfer blocks of information. Most programming languages, even those with no explicit Boolean type, have support for Boolean algebraic operations such as conjunction (AND, &, *), disjunction (OR, |, +), equivalence (EQV, =, ==), exclusive or/non-equivalence (XOR, NEQV, ^, !=), and negation (NOT, ~, !). In some languages, like Ruby, Smalltalk, and Alice the true and false values belong to separate classes, i.e., True and False, respectively, so there is no one Boolean type. In SQL, which uses a three-valued logic for explicit comparisons because of its special treatment of Nulls, the Boolean data type (introduced in SQL:1999) is also defined to include more than two truth values, so that SQL Booleans can store all logical values resulting from the evaluation of predicates in SQL. A column of Boolean type can also be restricted to just TRUE and FALSE though. One of the earliest programming languages to provide an explicit boolean data type was ALGOL 60 (1960) with values true and false and logical operators denoted by symbols ' ∧ {displaystyle wedge } ' (and), ' ∨ {displaystyle vee } ' (or), ' ⊃ {displaystyle supset } ' (implies), ' ≡ {displaystyle equiv } ' (equivalence), and ' ¬ {displaystyle eg } ' (not). Due to input device and character set limits on many computers of the time, however, most compilers used alternative representations for many of the operators, such as AND or 'AND'. This approach with boolean as a built-in (either primitive or otherwise predefined) data type was adopted by many later programming languages, such as Simula 67 (1967), ALGOL 68 (1970), Pascal (1970), Ada (1980), Java (1995), and C# (2000), among others. The first version of FORTRAN (1957) and its successor FORTRAN II (1958) had no logical values or operations; even the conditional IF statement took an arithmetic expression and branched to one of three locations according to its sign; see arithmetic IF. FORTRAN IV (1962), however, followed the ALGOL 60 example by providing a Boolean data type (LOGICAL), truth literals (.TRUE. and .FALSE.), Boolean-valued numeric comparison operators (.EQ., .GT., etc.), and logical operators (.NOT., .AND., .OR.). In FORMAT statements, a specific control character ('L') was provided for the parsing or formatting of logical values.