Bitwise Operators

Use cases

& Bitwise AND:

Compares each bit and returns 1 only if both values have 1 in the same position.

A: 5 // decimal
   101 // binary

B: 4 // decimal
   100 // binary

A & B

    101
&   100
---------
    100 // Only gives you one when both binary numbers have 1 in the same position

^ Bitwise XOR:

Exclusive OR: ≒ “difference detector”, only returns 1 when the bits are different.

0 ^ 0 = 0 // same, so returns 0
1 ^ 1 = 0 // same, so returns 0

1 ^ 0 = 1 // different, so returns 1
0 ^ 1 = 1 // different, so returns 1

C: 3 // decimal
   011 // binary

D: 5 // decimal
   101 // binary

C ^ D

    011
^   101
---------
    110 // Only gives you 1 when both are different from each other

| Bitwise OR:

Returns 1 if one of the bits is 1

E: 6 // decimal
   110 // binary

F: 2 // decimal
   010 // binary

E | F

    110
|   010
---------
    110 // Only returns 1 when either one is 1, because the last bit doesn't have 1 in either E or F, it is 0 

>> & << Bitwise Shift (Right and Left respectively):

>> Right Shift:

9 >> 2

9 -> 0b1001 // binary

>> 2 // shift bits to the right by 2

0b10(01) // will be removed (right shift)

0b1001 >> 2 -> 0b10

0b10 -> 2 // decimal

<< Left Shift:

10 << 2

10 -> 0b1010 // binary

<< 2 // shift bits to left by 2

0b1010(00) // 2 bits will be filled with zero, because of << "2"

0b1010 >> 2 -> 0b101000

0b101000 -> 40 // decimal

~ Bitwise Complement

10 -> 0b1010 // binary

~10 // bitwise complement

// Rule: 1 becomes 0, and vice versa
~10 -> 0b0101

With this, two’s complement is really easy, it’s just (~NUM) + 1.

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