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Boolean values are values that evaluate to either true
or false
, and are represented by the boolean
data type. Boolean expressions are very similar to mathematical expressions, but instead of using mathematical operators such as "+" or "", you use comparative or boolean operators such as "==" or "!".
Comparative operatorsEdit
Java has several operators that can be used to compare variables. For example, how would you tell if one variable has a greater value than another? The answer: use the "greaterthan" operator.
Here is a list of the comparative operators in Java:
>
: Greater than<
: Less than>=
: Greater than or equal to<=
: Less than or equal to==
: Equal to!=
: Not equal to
To see how these operators are used, look at this example:


Comparative operators can be used on any primitive types (except boolean
), but only the "equals" and "does not equal" operators work on objects. This is because the lessthan/greaterthan operators cannot be applied to objects, but the equivalency operators can.
Specifically, the == and != operators test whether both variables point to the same object. Objects will be covered later in the tutorial, in the "Classes, Objects, and Types" module. 
Boolean operatorsEdit
The Java boolean operators are based on the operations of the boolean algebra. The boolean operators operate directly on boolean values.
Here is a list of four common boolean operators in Java:
!
: Boolean NOT&&
: Boolean AND
: Boolean inclusive OR^
: Boolean exclusive XOR
The boolean NOT operator ("!") inverts the value of a boolean expression. The boolean AND operator ("&&") will result in true if and only if the values on both sides of the operator are true. The boolean inclusive OR operator ("") will result in true if either or both of the values on the sides of the operator is true. The boolean exclusive XOR operator ("^") will result in true if one and only of the values on the sides of the operator is true.
To show how these operators are used, here is an example:


Here are the truth tables for the boolean operators:
a  !a 

true  false 
false  true 
a  b  a && b  a  b  a ^ b 

true  true  true  true  false 
true  false  false  true  true 
false  true  false  true  true 
false  false  false  false  false 
 For help on simplifying complex logic, see De Morgan's laws.
In Java, boolean logic has a useful property called short circuiting. This means that expressions will only be evaluated as far as necessary. In the expression (a && b)
, if a is false, then b will not be evaluated because the expression will be false no matter what. Here is an example that shows that the second expression is not automatically checked:


To disable this property, you can use &
instead of &&
and 
instead of 
but it's not recommended.
 For the bitwise operations on
&
and
, see Arithmetic expressions.