# Boolean expressions

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 operators

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 "greater-than" 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: Code section 3.37: Comparisons. ```1 int a = 5, b = 3; 2 System.out.println(a > b); // Value is true because a is greater than b 3 System.out.println(a == b); // Value is false because a does not equal b 4 System.out.println(a != b); // Value is true because a does not equal b 5 System.out.println(b <= a); // Value is true because b is less than a ``` Output for code section 3.37 ```true false true true ```

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 less-than/greater-than 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 operators

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 one of the values on the sides of the operator is true.

To show how these operators are used, here is an example: Code section 3.38: Operands. ``` 1 boolean iMTrue = true; 2 boolean iMTrueToo = true; 3 boolean iMFalse = false; 4 boolean iMFalseToo = false; 5 6 System.out.println("NOT operand:"); 7 System.out.println(!iMTrue); 8 System.out.println(!iMFalse); 9 System.out.println(!(4 < 5)); 10 System.out.println("AND operand:"); 11 System.out.println(iMTrue && iMTrueToo); 12 System.out.println(iMFalse && iMFalseToo); 13 System.out.println(iMTrue && iMFalse); 14 System.out.println(iMTrue && !iMFalse); 15 System.out.println("OR operand:"); 16 System.out.println(iMTrue || iMTrueToo); 17 System.out.println(iMFalse || iMFalseToo); 18 System.out.println(iMTrue || iMFalse); 19 System.out.println(iMFalse || !iMTrue); 20 System.out.println("XOR operand:"); 21 System.out.println(iMTrue ^ iMTrueToo); 22 System.out.println(iMFalse ^ iMFalseToo); 23 System.out.println(iMTrue ^ iMFalse); 24 System.out.println(iMFalse ^ !iMTrue); ``` Output for code section 3.38 ```NOT operand: false true false AND operand: true false false true OR operand: true false true false XOR operand: false false true false ```

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: Code section 3.39: Short circuiting. ```1 System.out.println((4 < 5) || ((10 / 0) == 2)); ``` Output for code section 3.39 ```true ```

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.