Java, Java, Java

As we learned in Chapter 1, the boolean type is one of Java’s primitive types. For this type, there are only two possible values, true and false. The boolean type is derived from the work of British mathematician

George Boole, who in the 1850s, developed an algebra to process logical George Boole

expressions such as p and q. Such boolean expressions produce a value that is either true or false. Every modern programming language provides some means of representing boolean expressions.

The boolean type has several important uses. As we saw in Chap- ter 1, expressions of the form num == 7 and 5 < 7 have boolean val-

ues. Similarly, as we saw in Chapter 3, the boolean type is also used to Conditional statement

represent the condition in the if statement:

if (boolean expression) statement;

For this reason, boolean expressions are also called conditions. Along these same lines, a boolean variable can be used as a flag or a signal to “remem-

ber” whether or not a certain condition holds. For example, in the follow-Boolean flag

ing code fragment, we use isDone to mark when a particular process is completed:

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Boolean (or Logical) Operations

Like all the other simple data types, the boolean type consists of certain Data and operations

data—the values true and false—and certain actions or operations that can be performed on those data. For the boolean type there are four basic operations: AND (signified by &&), OR (signified by ), EXCLUSIVE-OR (signified by ), and NOT (signified by !). These are defined in the truth table shown in Table 5.1. A truth tables defines boolean operators by giving their values in all possible situations. The first two columns of the table give possible boolean values for two operands, o1 and o2. An operand is a value used in an operation. Note that each row gives a different value

 

assignment to the two operands, so that all possible assignments are repre- sented. The remaining columns give the values that result for the various operators given the assignment of values to o1 and o2.

 

TABLE 5.1 Truth-table definitions of the boolean operators: AND (&&), OR (||), EXCLUSIVE-OR (∧), and NOT (!)

o1o2o1 && o2o1 || o2o1 ∧ o2!o1

 

 

 

 

 

Binary operator

 

 

 

 

 

 

 

 

 

 

Unary operator

To see how to read this table, let’s look at the AND operation, which is defined in column 3. The AND operator is a binary operator—that is, it requires two operands, o1 and o2. If both o1 and o2 are true, then (o1 && o2) is true (row1). If either o1 or o2 or both o1 and o2 are false, then the expression (o1 && o2) is false (rows 2 and 3). The only case in which (o1 && o2) is true is when both o1 and o2 are true (row 4).

The boolean OR operation (column 4 of Table 5.1) is also a binary oper- ation. If both o1 and o2 are false, then (o1 o2) is false (row 4). If either o1 or o2 or both o1 and o2 are true, then the expression (o1 o2) is true (rows 1-3). Thus, the only case in which (o1 o2) is false is when both o1 and o2 are false.

The boolean EXCLUSIVE-OR operation (column 5 of Table 5.1) is a bi- nary operation, which differs from the OR operator in that it is true when either o1 or o2 is true (rows 2 and 3), but it is false when both o1 and o2 are true (row 1).

The NOT operation (the last column of Table 5.1) is a unary operator— it takes only one operand—and it simply reverses the truth value of its operand. Thus, if o1 is true, !o1 is false, and vice versa.

Precedence and Associativity

In order to evaluate complex boolean expressions, it is necessary to un- derstand the order in which boolean operations are carried out by the computer. For example, what is the value of the following expression?

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The value of this expression depends on whether we evaluate the first or the && first. If we evaluate the first, the expression’s value will be false; if we evaluate the && first, the expression’s value will be true. In the following example, we use parentheses to force one operation to be done before the other:

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As these evaluations show, we can use parentheses to force one operator

or the other to be evaluated first. However, in Java, the && operator has Parentheses supersede

higher precedence than the operator. Therefore, the second alternative corresponds to the default interpretation that Java would apply to the ex- pression that has no parentheses. In other words, given the expression true true && f alse, the AND operation would be evaluated before the OR operation even though the OR operator occurs first (i.e., to the left) in the unparenthesized expression.

 

TABLE 5.2 Precedence order of the boolean operators Precedence OrderOperatorOperation

( )Parentheses

!NOT

EXCLUSIVE-OR

&&AND

||OR

 

As this example illustrates, the boolean operators have a built-in prece- dence order which is used to determine how boolean expressions are to be evaluated (Table 5.2). A simple method for evaluating an expression is to parenthesize the expression and then evaluate it. For example, to evaluate the complex expression

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we would first parenthesize it according to the precedence rules set out in Table 5.2, which gives the following expression:

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We can then evaluate this fully parenthesized expression, step by step, starting at the innermost parentheses:

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In addition to operator precedence, it is necessary to know about an operator’s associativity in order to evaluate boolean expressions of the form (op1 || op2 || op3). Should this expression be evaluated as

 

((op1 op2) op3) or as (op1 (op2 op3))? The binary boolean opera- tors all associate from left to right. Thus, the expressions

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would be evaluated as follows:

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Short-Circuit Evaluation

 

Another important feature of the boolean operators is that they utilize a form of evaluation known as short-circuit evaluation. In short-circuit eval- uation, a boolean expression is evaluated from left to right, and the evalu- ation is discontinued as soon as the expression’s value can be determined, regardless of whether it contains additional operators and operands. For example, in the expression

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if expr1 is false, then the AND expression must be false, so expr2 need not evaluated. Similarly, in the expression

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if expr1 is true, then the OR expression must be true, so expr2 need not evaluated.

In addition to being a more efficient form of evaluating boolean ex- pressions, short-circuit evaluation has some practical uses. For example, we can use short-circuit evaluation to guard against null pointer excep- tions. Recall from Chapter 2 that a null pointer exception results when you try to use an uninstantiated reference variable—that is, a reference variable that has not been assigned an object. For example, if we declare a OneRowNim variable without instantiating it and then try to use it, a null pointer exception will result:

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In this code, a null pointer exception results when we use game in the method call game.gameOver(). We can use short-circuit evaluation to prevent the exception from occurring:

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In this case, because game != null is false, neither method call involv- ing game is made, thus avoiding the exception.