## 1. Overview

Operators are used in the Java language to operate on data and variables.

In this tutorial, we’ll explore Bitwise Operators and how they work in Java.

## 2. Bitwise Operators

**Bitwise operators work on binary digits or bits of input values.** We can apply these to the integer types – *long, int, short, char,* and *byte.*

Before exploring the different bitwise operators let’s first understand how they work.

**Bitwise operators work on a binary equivalent of decimal numbers and perform operations on them bit by bit as per the given operator:**

- First, the operands are converted to their binary representation
- Next, the operator is applied to each binary number and the result is calculated
- Finally, the result is converted back to its decimal representation

Let’s understand with an example; let’s take two *integers:*

```
int value1 = 6;
int value2 = 5;
```

Next, let’s apply a bitwise OR operator on these numbers:

`int result = 6 | 5;`

To perform this operation, first, the binary representation of these numbers will be calculated:

```
Binary number of value1 = 0110
Binary number of value2 = 0101
```

Then the operation will be applied to each bit. The result returns a new binary number:

```
0110
0101
-----
0111
```

Finally, the result *0111 *will be converted back to decimal which is equal to *7*:

`result : 7`

Bitwise operators are further classified as bitwise logical and bitwise shift operators. Let’s now go through each type.

## 3. Bitwise Logical Operators

The bitwise logical operators are AND(&), OR(|), XOR(^), and NOT(~).

### 3.1. Bitwise *OR* (|)

**The OR operator compares each binary digit of two integers and gives back 1 if either of them is 1.**

This is similar to the || logical operator used with booleans. When two booleans are compared the result is *true* if either of them is *true.* Similarly, the output is 1 when either of them is 1.

We saw an example of this operator in the previous section:

```
@Test
public void givenTwoIntegers_whenOrOperator_thenNewDecimalNumber() {
int value1 = 6;
int value2 = 5;
int result = value1 | value2;
assertEquals(7, result);
}
```

Let’s see the binary representation of this operation:

```
0110
0101
-----
0111
```

Here, we can see that using OR, 0 and 0 will result in 0, while any combination with at least a 1 will result in 1.

### 3.2. Bitwise *AND* (&)

**The AND operator compares each binary digit of two integers and gives back 1 if both are 1, otherwise it returns 0.**

This is similar to the && operator with *boolean* values. When the values of two *booleans* are *true* the result of a && operation is *true.*

Let’s use the same example as above, except now using the & operator instead of the | operator:

```
@Test
public void givenTwoIntegers_whenAndOperator_thenNewDecimalNumber() {
int value1 = 6;
int value2 = 5;
int result = value1 & value2;
assertEquals(4, result);
}
```

Let’s also see the binary representation of this operation:

```
0110
0101
-----
0100
```

*0100* is *4* in decimal, therefore, the result is:

`result : 4`

### 3.3. Bitwise XOR (^)

**The XOR operator compares each binary digit of two integers and gives back 1 if both the compared bits are different.** This means that if bits of both the integers are 1 or 0 the result will be 0; otherwise, the result will be 1:

```
@Test
public void givenTwoIntegers_whenXorOperator_thenNewDecimalNumber() {
int value1 = 6;
int value2 = 5;
int result = value1 ^ value2;
assertEquals(3, result);
}
```

And the binary representation:

```
0110
0101
-----
0011
```

*0011 *is 3 in decimal, therefore, the result is:

`result : 3`

### 3.4. Bitwise COMPLEMENT (~)

**Bitwise Not or Complement operator simply means the negation of each bit of the input value. It takes only one integer and it’s equivalent to the ! operator.**

This operator changes each binary digit of the integer, which means all 0 become 1 and all 1 become 0. The ! operator works similarly for *boolean* values: it reverses *boolean* values from *true* to *false* and vice versa.

Now let’s understand with an example how to find the complement of a decimal number.

Let’s do the complement of value1 = 6:

```
@Test
public void givenOneInteger_whenNotOperator_thenNewDecimalNumber() {
int value1 = 6;
int result = ~value1;
assertEquals(-7, result);
}
```

The value in binary is:

`value1 = 0000 0110`

By applying the complement operator, the result will be:

`0000 0110 -> 1111 1001`

This is the one’s complement of the decimal number 6. And since the first (leftmost) bit is 1 in binary, it means that the sign is negative for the number that is stored.

Now, since the numbers are stored as 2’s complement, first we need to find its 2’s complement and then convert the resultant binary number into a decimal number:

`1111 1001 -> 0000 0110 + 1 -> 0000 0111`

Finally, 0000 0111 is 7 in decimal. Since the sign bit was 1 as mentioned above, therefore the resulting answer is:

`result : -7`

### 3.5. Bitwise Operator Table

Let’s summarize the result of the operators we’ve seen to so far in a comparison table:

```
A B A|B A&B A^B ~A
0 0 0 0 0 1
1 0 1 0 1 0
0 1 1 0 1 1
1 1 1 1 0 0
```

## 4. Bitwise Shift Operators

**Binary shift operators shift all the bits of the input value either to the left or right based on the shift operator.**

Let’s see the syntax for these operators:

`value <operator> <number_of_times>`

The left side of the expression is the integer that is shifted, and the right side of the expression denotes the number of times that it has to be shifted.

Bitwise shift operators are further classified as bitwise left and bitwise right shift operators.

### 4.1. Signed Left Shift [<<]

**The left shift operator shifts the bits to the left by the number of times specified by the right side of the operand. After the left shift, the empty space in the right is filled with 0.**

Another important point to note is that **shifting a number by one is equivalent to multiplying it by 2, or, in general, left shifting a number by ***n* positions is equivalent to multiplication by 2^*n*.

Let’s take the value 12 as the input value.

Now, we will move it by 2 places to the left (12 <<2) and see what will be the final result.

The binary equivalent of 12 is 00001100. After shifting to the left by 2 places, the result is 00110000, which is equivalent to 48 in decimal:

```
@Test
public void givenOnePositiveInteger_whenLeftShiftOperator_thenNewDecimalNumber() {
int value = 12;
int leftShift = value << 2;
assertEquals(48, leftShift);
}
```

This works similarly for a negative value:

```
@Test
public void givenOneNegativeInteger_whenLeftShiftOperator_thenNewDecimalNumber() {
int value = -12;
int leftShift = value << 2;
assertEquals(-48, leftShift);
}
```

### 4.2. Signed Right Shift [>>]

**The right shift operator shifts all the bits to the right.** The empty space in the left side is filled depending on the input number:

**When an input number is negative, where the leftmost bit is 1, then the empty spaces will be filled with 1**
**When an input number is positive, where the leftmost bit is 0, then the empty spaces will be filled with 0**

Let’s continue the example using 12 as input.

Now, we will move it by 2 places to the right(12 >>2) and see what will be the final result.

The input number is positive, so after shifting to the right by 2 places, the result is 0011, which is 3 in decimal:

```
@Test
public void givenOnePositiveInteger_whenSignedRightShiftOperator_thenNewDecimalNumber() {
int value = 12;
int rightShift = value >> 2;
assertEquals(3, rightShift);
}
```

Also, for a negative value:

```
@Test
public void givenOneNegativeInteger_whenSignedRightShiftOperator_thenNewDecimalNumber() {
int value = -12;
int rightShift = value >> 2;
assertEquals(-3, rightShift);
}
```

### 4.3. Unsigned Right Shift [>>>]

This operator is very similar to the signed right shift operator. **The only difference is that the empty spaces in the left are filled with 0 irrespective of whether the number is positive or negative.** Therefore, the result will always be a positive integer.

Let’s right shift the same value of 12:

```
@Test
public void givenOnePositiveInteger_whenUnsignedRightShiftOperator_thenNewDecimalNumber() {
int value = 12;
int unsignedRightShift = value >>> 2;
assertEquals(3, unsignedRightShift);
}
```

And now, the negative value:

```
@Test
public void givenOneNegativeInteger_whenUnsignedRightShiftOperator_thenNewDecimalNumber() {
int value = -12;
int unsignedRightShift = value >>> 2;
assertEquals(1073741821, unsignedRightShift);
}
```

## 5. Difference Between Bitwise and Logical Operators

There are a few differences between the bitwise operators we’ve discussed here and the more commonly known logical operators.

First, **logical operators work on ***boolean* expressions and return *boolean* values (either *true* or *false),* whereas **bitwise operators work on binary digits** of integer values (*long, int, short, char,* and *byte*) and return an integer.

Also, logical operators always evaluate the first *boolean* expression and, depending on its result and the operator used, may or may not evaluate the second. On the other hand, **bitwise operators always evaluate both operands**.

Finally, logical operators are used in making decisions based on multiple conditions, while bitwise operators work on bits and perform bit by bit operations.

**6. Use Cases**

Some potential use cases of bitwise operators are:

- Communication stacks where the individual bits in the header attached to the data signify important information
- In embedded systems to set/clear/toggle just one single bit of a specific register without modifying the remaining bits
- To encrypt data for safety issues using the XOR operator
- In data compression by converting data from one representation to another, to reduce the amount of space used

## 7. Conclusion

In this tutorial, we learned about the types of bitwise operators and how they’re different from logical operators. We also saw some potential use cases for them.

All the code examples in this article are available over on GitHub.