How do shift operators work in Java?

I am trying to understand the shift operators and couldn't get much. When I tried to execute the below code

System.out.println(Integer.toBinaryString(2 << 11));
System.out.println(Integer.toBinaryString(2 << 22));
System.out.println(Integer.toBinaryString(2 << 33));
System.out.println(Integer.toBinaryString(2 << 44));
System.out.println(Integer.toBinaryString(2 << 55));

I get the below

1000000000000    
100000000000000000000000    
100    
10000000000000    
1000000000000000000000000    

Could somebody please explain?

System.out.println(Integer.toBinaryString(2 << 11)); 

Shifts binary 2(10) by 11 times to the left. Hence: 1000000000000

System.out.println(Integer.toBinaryString(2 << 22)); 

Shifts binary 2(10) by 22 times to the left. Hence : 100000000000000000000000

System.out.println(Integer.toBinaryString(2 << 33)); 

Now, int is of 4 bytes,hence 32 bits. So when you do shift by 33, it's equivalent to shift by 1. Hence : 100

2 from decimal numbering system in binary is as follows

10

now if you do

2 << 11

it would be , 11 zeros would be padded on the right side

1000000000000

>The signed left shift operator "<<" shifts a bit pattern to the left, and the signed right shift operator ">>" shifts a bit pattern to the right. The bit pattern is given by the left-hand operand, and the number of positions to shift by the right-hand operand. The unsigned right shift operator ">>>" shifts a zero into the leftmost position, while the leftmost position after ">>" depends on sign extension [..]

left shifting results in multiplication by 2 (*2) in terms or arithmetic

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For example

2 in binary 10, if you do <<1 that would be 100 which is 4

4 in binary 100, if you do <<1 that would be 1000 which is 8

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Also See

• absolute-beginners-guide-to-bit-shifting

Right and Left shift work on same way here is How Right Shift works; The Right Shift: The right shift operator, >>, shifts all of the bits in a value to the right a specified number of times. Its general form:

value >> num

Here, num specifies the number of positions to right-shift the value in value. That is, the >> moves all of the bits in the specified value to the right the number of bit positions specified by num. The following code fragment shifts the value 32 to the right by two positions, resulting in a being set to 8:

int a = 32;
a = a >> 2; // a now contains 8

When a value has bits that are “shifted off,” those bits are lost. For example, the next code fragment shifts the value 35 to the right two positions, which causes the two low-order bits to be lost, resulting again in a being set to 8.

int a = 35;
a = a >> 2; // a still contains 8

Looking at the same operation in binary shows more clearly how this happens:

00100011 35 >> 2
00001000 8

Each time you shift a value to the right, it divides that value by two—and discards any remainder. You can take advantage of this for high-performance integer division by 2. Of course, you must be sure that you are not shifting any bits off the right end. When you are shifting right, the top (leftmost) bits exposed by the right shift are filled in with the previous contents of the top bit. This is called sign extension and serves to preserve the sign of negative numbers when you shift them right. For example, –8 >> 1 is –4, which, in binary, is

11111000 –8 >>1
11111100 –4

It is interesting to note that if you shift –1 right, the result always remains –1, since sign extension keeps bringing in more ones in the high-order bits. Sometimes it is not desirable to sign-extend values when you are shifting them to the right. For example, the following program converts a byte value to its hexadecimal string representation. Notice that the shifted value is masked by ANDing it with 0x0f to discard any sign-extended bits so that the value can be used as an index into the array of hexadecimal characters.

// Masking sign extension.
class HexByte {
  static public void main(String args[]) {
    char hex[] = {
      '0', '1', '2', '3', '4', '5', '6', '7',
      '8', '9', 'a', 'b', 'c', 'd', 'e', 'f'
    };
  byte b = (byte) 0xf1;
 System.out.println("b = 0x" + hex[(b >> 4) & 0x0f] + hex[b & 0x0f]);
}
}

Here is the output of this program:

b = 0xf1

I believe this might Help:

    System.out.println(Integer.toBinaryString(2 << 0));
    System.out.println(Integer.toBinaryString(2 << 1));
    System.out.println(Integer.toBinaryString(2 << 2));
    System.out.println(Integer.toBinaryString(2 << 3));
    System.out.println(Integer.toBinaryString(2 << 4));
    System.out.println(Integer.toBinaryString(2 << 5));

Result

    10
    100
    1000
    10000
    100000
    1000000

Edited:

Must Read This (how-do-the-bitwise-shift-operators-work)

I think it would be the following, for example:

• Signed left shift

[ 2 << 1 ] is => [10 (binary of 2) add 1 zero at the end of the binary string] Hence 10 will be 100 which becomes 4.

Signed left shift uses multiplication... So this could also be calculated as 2 * (2^1) = 4. Another example [2 << 11] = 2 *(2^11) = 4096

• Signed right shift

[ 4 >> 1 ] is => [100 (binary of 4) remove 1 zero at the end of the binary string] Hence 100 will be 10 which becomes 2.

Signed right shift uses division... So this could also be calculated as 4 / (2^1) = 2 Another example [4096 >> 11] = 4096 / (2^11) = 2

It will shift the bits by padding that many 0's.

For ex,

• binary 10 which is digit 2 left shift by 2 is 1000 which is digit 8
• binary 10 which is digit 2 left shift by 3 is 10000 which is digit 16

The shift can be implement with data types (char, int and long int). The float and double data connot be shifted.

value= value >> steps  // Right shift, signed data.
value= value << steps  // Left shift, signed data.

Signed left shift Logically Simple if 1<<11 it will tends to 2048 and 2<<11 will give 4096

In java programming int a = 2 << 11;

// it will result in 4096

2<<11 = 2*(2^11) = 4096

The typical usage of shifting a variable and assigning back to the variable can be rewritten with shorthand operators <<=, >>=, or >>>=, also known in the spec as Compound Assignment Operators.

For example,

i >>= 2

produces the same result as

i = i >> 2