Julia: Bitwise operators

Following are the bitwise operators supported by Julia.

Operator	Description
~	Bit wise not
&	Bit wise and
|	Bit wise or
$	Bit wise XOR
>>>	Zero fill right shift
>>	Right shift
<<	Left shift

Before discuss about the Bit wise operators in detail, will discuss about Binary representations of a number

1's Complement

1's complement simply inverts the bits, if the bit is set to zero, it sets the bit to 1 and if the bit is set to 1 it sets the bit to zero.

Ex:

8 in binary            = 0 0 0 0 1 0 0 0

1's complement(8) = 1 1 1 1 0 1 1 1

2's complement

Negative numbers are stored in 2's complement form. i.e., -8 is 2's complement of 8.

2's complement is sum of (1's complement of a number + 1)

Ex:

8 in binary            = 0 0 0 0 1 0 0 0

1's complement(8) = 1 1 1 1 0 1 1 1

2's complement(8) =               (+) 1

                               -----------------

                                1 1 1 1 1 0 0 0

                                ----------------

There fore -8 in 2's complement form is 11111000

Bit wise not (~)

Inversion operator change the bit value to zero, if it is one and change the bit value to one if it is zero.

Example

a = 7;

a in binary format is       0 0 0 0 0 1 1 1

~(a) in binary format is  1 1 1 1 1 0 0 0

~(a) represents -8 in binary format.

julia> a=7

7

julia> ~a

-8

Bit wise and(&), or(|), Ex-OR($)

Bit1	Bit2	&	|	$
0	0	0	0	0
0	1	0	1	1
1	0	0	1	1
1	1	1	1	0

julia> a&b
8

julia> a|b
9

julia> a$b
1

Explanation

   a    = 0000 1000

   b    = 0000 1001

   a&b = 0000 1000

   a    = 0000 1000

   b    = 0000 1001

   a|b = 0000 10001

   a     = 0000 1000

   b     = 0000 1001

   a^b = 0000 0001

Bit Wise Left Shift(<<)

Left shift operator shifts all the bits to one bit left, i.e, it doubles the value.

Syntax:

    variable << n

    left shift the variable by 'n' number of times.

    Variable << n is equals to variable = variable * 2^n

var = 2;

var << 1 = 2 * 2^1 = 4

var << 2 = 2 * 2^2 = 8

var << 9 = 2 * 2^9 = 1024

julia> a=2;

julia> a<<1
4

julia> a<<2
8

julia> a<<3
16

Bit Wise Right Shift(>>)

Right shift operator shifts all the bits to one bit right, i.e, it half (divide by 2) the value.

Syntax:

variable >> n : Right shift the variable by 'n' number of times.

Variable >> n is equals to variable = variable / 2^n

   var = 128;

   var >> 1 = 128 / (2^1) = 64

   var >> 2 = 128 / (2^2) = 32

julia> var = 128;

julia> var>>1
64

julia> var>>2
32

Bit Wise unsigned Right Shift(>>>)
Shifts all the bits to one bit right, and make the left most bit to zero.

julia> var=-128
-128

julia> var>>>1
9223372036854775744

Explanation

-128 is represented in binary like “1111111111111111111111111111111111111111111111111111111110000000”

So (-128>>>1) is like below sequence.

0111111111111111111111111111111111111111111111111111111111000000

julia> bits(9223372036854775744)
"0111111111111111111111111111111111111111111111111111111111000000"

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