A computer stores data in binary. In other words, information is encoded as a sequence of 1’s and 0’s. On most computers, the memory is organized into 8-bit cells known as bytes.
Java defines several operators that allow you to work at the binary level. These operators perform bit-by-bit (commonly known as bitwise) operations on bit patterns and involve manipulation of individual bits. Such operators are known as bitwise operators. These operators can be applied only to integers.
The bitwise AND operator combines two bits and returns true
only if both the bits are true. Otherwise, it returns false for
the given bit pair. When I say true and false, I mean 1 and 0, respectively.
The operator basically combines all the bits in the given operands.
This operator is called the bitwise AND because the left hand side bit and the right hand side bit must be true for the operator to return true.
Here’s the truth table for the bitwise AND operator.
| X | Y | Z |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Mathematically, it is written as Z = X . Y where . implies multiplication.
In a bitwise operation, the smaller sized operand is padded with zeroes before the most significant bit to match the larger sized operand.
Consider the following example.
public class BitwiseAndExample {
public static void main(String[] arguments) {
short a = 10;
int b = 255;
int c = a & b;
System.out.println(c);
}
}
We know that short variables occupy 16 bits and integer variables occupy 32 bits.
To evaluate the last expression, first a is padded with 16 zeroes on the left to convert it to 32-bits.
Then each bit is combined to produce 0 or 1 if the corresponding bits are 1 or otherwise, respectively.
The bitwise OR operator combines two bits and returns true if at least one of the bits is true.
Otherwise, it returns false for the given bit pair. Again, when I say true and alse, I mean 1
and 0, respectively
The operator basically combines all the bits in the given operands.
This operator is called the bitwise OR because the left hand side bit or the right hande side bit must be true for the operator to return true. Further, by definition it returns true if both the bits are true and returns false if both the bits are false.
Here’s the truth table for the bitwise OR operator.
| X | Y | Z |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Mathematically, it is written as Z = X + Y where . implies addition.
As metioned previously, in a bitwise operation, the smaller sized operand is padded with zeroes before the most significant bit to match the larger sized operand.
Consider the following example.
short a = 19;
int b = 7;
int c = a | b;
We know that short variables occupy 16 bits and integer variables occupy 32 bits.
To evaluate the last expression, first a is padded with 16 zeroes on the left to convert it to 32-bits.
Then each bit is combined to produce 1 or 0 if at least one of the corresponding bits is 1 or otherwise, respectively.
The bitwise XOR operator combines two bits and returns true only if one of the bits is true and
the other bit is false. Otherwise, it returns false for the given bit pair. Again, when we say
true and false, we mean 1 and 0, respectively The operator basically combines all the bits in
the given operands.
This operator is called the bitwise XOR because the left hand side bit must be exclusive of the right hande side bit for the operator to return true. Further, by definition it returns false if both the bits are true or false.
Here’s the truth table for the bitwise OR operator.
| X | Y | Z |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Mathematically, it is written as Z = X . ~Y + ~X . Y where . implies multiplication.
As metioned previously, in a bitwise operation, the smaller sized operand is padded with zeroes before the most significant bit to match the larger sized operand.
Consider the following example.
short a = 25;
int b = 25;
int c = a ^ b;
We know that short variables occupy 16 bits and integer variables occupy 32 bits.
To evaluate the last expression, first a is padded with 16 zeroes on the left to convert it to 32-bits.
Then each bit is combined to produce 1 or 0 if the corresponding bits are exclusive or otherwise, respectively.
The bitwise complement operator is a unary operator. It flips every bit in the operand.
Here’s the truth table for the bitwise complement operator.
| X | Y |
|---|---|
| 0 | 1 |
| 1 | 0 |
Mathematically, it is written as Y = ~X, where ~ implies negation.
Consider the following example.
int a = 255;
int b = ~a;
Here, each bit is flipped to produce 1 or 0 if the corresponding bit is 0 or 1, respectively.
The content in this section may be wrong. I need to research and verify the content.
The left shift operator << shifts all of the bits in the first operand to
the left by a number of times specified by the second operand.
It has the following general form.
value << times
Where, times specifies the number of positions to left-shift the specified value.
For each shift, the most significant bit is shifted out and lost. A zero is brought in as the least significant bit.
This means that when you left shift an integer operand, bits are lost after 32 positions.
The right shift operator >> shifts all of the bits in the first operand to
the right by a number of times specified by the second operand.
It has the following general form.
value >> times
Where, times specifies the number of positions to right-shift the specified value.
For each shift, the least significant bit is shifted out and lost. A zero is brought in as the most significant bit.
This means that when you right shift an integer operand, bits are lost after 32 positions.