Differences in boolean operators: & vs && and | vs ||

Question

Those are the bitwise AND and bitwise OR operators.

int a = 6; // 110
int b = 4; // 100

// Bitwise AND    

int c = a & b;
//   110
// & 100
// -----
//   100

// Bitwise OR

int d = a | b;
//   110
// | 100
// -----
//   110

System.out.println(c); // 4
System.out.println(d); // 6

Thanks to Carlos for pointing out the appropriate section in the Java Language Spec (15.22.1, 15.22.2) regarding the different behaviors of the operator based on its inputs.

Indeed when both inputs are boolean, the operators are considered the Boolean Logical Operators and behave similar to the Conditional-And (&&) and Conditional-Or (||) operators except for the fact that they don't short-circuit so while the following is safe:

if((a != null) && (a.something == 3)){
}

This is not:

if((a != null) & (a.something == 3)){
}

"Short-circuiting" means the operator does not necessarily examine all conditions. In the above examples, && will examine the second condition only when a is not null (otherwise the whole statement will return false, and it would be moot to examine following conditions anyway), so the statement of a.something will not raise an exception, or is considered "safe."

The & operator always examines every condition in the clause, so in the examples above, a.something may be evaluated when a is in fact a null value, raising an exception.

I think you're talking about the logical meaning of both operators, here you have a table-resume:

boolean a, b;

Operation     Meaning                       Note
---------     -------                       ----
   a && b     logical AND                    short-circuiting
   a || b     logical OR                     short-circuiting
   a &  b     boolean logical AND            not short-circuiting
   a |  b     boolean logical OR             not short-circuiting
   a ^  b     boolean logical exclusive OR
  !a          logical NOT

short-circuiting        (x != 0) && (1/x > 1)   SAFE
not short-circuiting    (x != 0) &  (1/x > 1)   NOT SAFE

Short-circuit evaluation, minimal evaluation, or McCarthy evaluation (after John McCarthy) is the semantics of some Boolean operators in some programming languages in which the second argument is executed or evaluated only if the first argument does not suffice to determine the value of the expression: when the first argument of the AND function evaluates to false, the overall value must be false; and when the first argument of the OR function evaluates to true, the overall value must be true.

Not Safe means the operator always examines every condition in the clause, so in the examples above, 1/x may be evaluated when the x is, in fact, a 0 value, raising an exception.

I know there's a lot of answers here, but they all seem a bit confusing. So after doing some research from the Java oracle study guide, I've come up with three different scenarios of when to use && or &. The three scenarios are logical AND, bitwise AND, and boolean AND.

Logical AND: Logical AND (aka Conditional AND) uses the && operator. It's short-circuited meaning: if the left operand is false, then the right operand will not be evaluated.
Example:

int x = 0;
if (false && (1 == ++x) {
    System.out.println("Inside of if");
}
System.out.println(x); // "0"

In the above example the value printed to the console of x will be 0, because the first operand in the if statement is false, hence java has no need to compute (1 == ++x) therefore x will not be computed.

Bitwise AND: Bitwise AND uses the & operator. It's used to preform a bitwise operation on the value. It's much easier to see what's going on by looking at operation on binary numbers ex:

int a = 5;     //                    5 in binary is 0101
int b = 12;    //                   12 in binary is 1100
int c = a & b; // bitwise & preformed on a and b is 0100 which is 4

As you can see in the example, when the binary representations of the numbers 5 and 12 are lined up, then a bitwise AND preformed will only produce a binary number where the same digit in both numbers have a 1. Hence 0101 & 1100 == 0100. Which in decimal is 5 & 12 == 4.

Boolean AND: Now the boolean AND operator behaves similarly and differently to both the bitwise AND and logical AND. I like to think of it as preforming a bitwise AND between two boolean values (or bits), therefore it uses & operator. The boolean values can be the result of a logical expression too.

It returns either a true or false value, much like the logical AND, but unlike the logical AND it is not short-circuited. The reason being, is that for it to preform that bitwise AND, it must know the value of both left and right operands. Here's an ex:

int x = 0;
if (false & (1 == ++x) {
    System.out.println("Inside of if");
}
System.out.println(x); //"1"

Now when that if statement is ran, the expression (1 == ++x) will be executed, even though the left operand is false. Hence the value printed out for x will be 1 because it got incremented.

This also applies to Logical OR (||), bitwise OR (|), and boolean OR (|) Hope this clears up some confusion.

The operators && and || are short-circuiting, meaning they will not evaluate their right-hand expression if the value of the left-hand expression is enough to determine the result.

& and | provide the same outcome as the && and || operators. The difference is that they always evaluate both sides of the expression where as && and || stop evaluating if the first condition is enough to determine the outcome.

In Java, the single operators &, |, ^, ! depend on the operands. If both operands are ints, then a bitwise operation is performed. If both are booleans, a "logical" operation is performed.

If both operands mismatch, a compile time error is thrown.

The double operators &&, || behave similarly to their single counterparts, but both operands must be conditional expressions, for example:

if (( a < 0 ) && ( b < 0 )) { ... } or similarly, if (( a < 0 ) || ( b < 0 )) { ... }

source: java programming lang 4th ed

& and | are bitwise operators on integral types (e.g. int): http://download.oracle.com/javase/tutorial/java/nutsandbolts/op3.html

&& and || operate on booleans only (and short-circuit, as other answers have already said).