13. Operators ( Bitwise ).md

13. Operators ( Bitwise )

Bitwise Operators can be applied to the Integer types: long , int , short , char , byte

Operator	Operation
~	Bitwise unary NOT
&	Bitwise AND
^	Bitwise exclusive OR
>>	Shift Right
>>>	Shift Right zero fill
<<	Shift left
&=	Bitwise AND assignment
	=
^=	Bitwise exclusive OR assignment
>> =	Shift right assignment
>>> =	Shift right zero fill assignment
<< =	shift left assignment

(Signed) Left shift ( << )

(Signed) Right shift ( >> )

Unsigned Right Shift ( >>> )

Left Shift ( << )

• Convert number to binary ( if not binary ).
• Move the numbers to the left and replace least significant bits with zero.
• Eg: 20 << 4 (320)

1. Assume 8 bit system ( 20 ⇒ 0b00010100 )
2. shifting four positions to left and fill least significant bits with 0. i.e; simply add four zeroes at the end
    0b000101000000 ⇒ 0b101000000
3. 0b101000000 = 320

💡 formula: **x << n ⇒ x * ( 2 ^ n )**

Ex: 20 << 4 = 20 * ( 2 ^ 4 ) = 20 * 16 = 320

Right shift ( >> )

• convert number to binary.
• Move the numbers to the right and replace most significant bits with signed value.
• Ex: 20 >> 4 (1)

1. Assume 8 bit system ( 20 ⇒ 0b00010100 )
2. shifting four positions to right and replace most significant bits 
    with 0 (signed bit) 
    i.e; simply remove last 4 bits and add 4 sign bits 0 at the beginning

    0b00010100 => 0b00000001 => 1

• Ex: -20 >> 4 ( -2 )

1. Assume 8 bit system ( 20 ⇒ 0b00010100 ) ( -20 ⇒ 0b11101100 ) using 2’s compliment method
2. shifting four positions to right and replace most significant bits with 1(signed bit) 
    i.e; simply add 4 sign bits 1 at the beginning and  remove last 4 bits
    
    0b11111110 ⇒ using 2’s compliment ⇒ 0b00000010 ⇒ - 2

💡 formula: x >> n ⇒ Math.floor(x / ( 2 ^ n ))

Ex:    
20 >> 4 ⇒ floor(20 / 2 ^4 ) ⇒ 20/16 ⇒ floor(1.xxx) ⇒ 1
-20 >> 4 ⇒ floor(-20 / 2 ^4 ) ⇒ -20/16 ⇒ floor(-1.xxx) ⇒ -2

Unsigned Right Shift ( >>> ) ( sign is not preserved )

• convert number to binary.
• Move the numbers to the right and replace most significant bits with 0.
• Ex: 20 >>> 4 (1) ( same as signed right shift for positive number )

1. Assume 8 bit system ( 20 ⇒ 0b00010100 )
2. shifting four positions to right and replace most significant bits with 0
   i.e; simply remove last 4 bits and add 4 zeros at the beginning
    0b00010100 => 0b00000001
3. 0b00000001 ⇒  1

• Ex: -20 >>> 4 (268435454)

1. Assume 8 bit system ( 20 ⇒ 0b00010100 ) ( -20 ⇒ 0b11101100 ) using 2’s 
	 compliment method
2. shifting four positions to right and replace most significant bits with 0 
   i.e; simply add 4 zeros at the beginning and remove last 4 bits

    0b00001110 ⇒ 14
    -20 => 0b11111111111111111111111111101100 ( 32 bit system )
    0b11111111111111111111111111101100 >>> 4
    0b00001111111111111111111111111110 => 268435454 ( Decimal )