What Does the Operator ^ Mean in Java?

Bitwise Logical Operations work on binary representations of values

In computer programming languages, operators represent a particular operation the computer should perform on a value. Many of these operators correspond with mathematical operations such as addition or division. As a modern programming language, Java is no different. Java also includes many operators that perform more esoteric mathematical functions geared particularly toward computers, such as logical operators AND ("&&") and OR ("||"). Java also contains operators such as the "^" symbol, representing the bitwise exclusive OR operation.

Java and Logic

Java uses logical operations as part of its structure. The flow of a Java program depends on the evaluation of "conditionals" in which the program evaluates a value as either "true" or "false." For example, the comparison "3 < 4" evaluates as "true" because three is less than four. But, "3 > 4" evaluates to false. These simple conditionals can help control the flow of a program by forcing the code to make decisions about program state. The following statement, for example, shows an "if" statement. If the condition in the parentheses is true, then the if statement executes. It does not if the value is false.

if (3 < 4) //true, "if" executes

Complex Conditionals

In order to move beyond simple conditionals involving one comparison, Java uses logical operators to join conditions into larger statements. One of these operators is the OR operator. The OR operator ("||") joins two conditions, and returns a true or false value depending on those values. If one or both values evaluate as true, then the OR operation returns a true. Otherwise, it returns false. Given two comparisons, the following if statements will either execute or not based on the result of the OR operations:

if (3 < 4 || 3 > 4) //first condition is true, second false, the OR operation returns true

if (3 > 4 || 3 > 5) //both conditions are false, OR returns false

Bitwise OR

In computing, truth values are often represented in binary, with the number 0 representing "false" and the number "1" representing "true." Following this, programmers can use logical operations on the binary representations of values to manipulate them. For example, the integer 5 is stored into a computer as a binary number, 0101. The number 4 is stored in binary as 0100. A bitwise OR operation compares each digit and returns a result: If one or both of the digits is 1, then OR returns 1. Else, it returns 0 (as in the following example):

0101

0100 OR

-----------

0101 = 5

Bitwise Exclusive OR

The bitwise exclusive OR represented by the "^" symbol performs similarily to the bitwise OR, with one small difference. The exclusive OR returns a 1 value if the values are different, and a 0 if they are the same. Using the binary examples of 0101 and 0100, the bitwise exclusive OR operation looks like this:

0101

0100 XOR

------------

0001 = 1

And in Java, the following code performs the same operation, using the "^" symbol:

int x = 5 ^ 4; //x = 1

References

• Oracle: Equality, Relational, and Conditional Operators
• IBM: Bitwise Exclusive OR