Bitwise Operation

Example Binary numbers

3    = 000011
5    = 000101
10   = 001010

Bitwise AND

Take two numbers, line them up on top of each other, and create a new number that has a 1 where both numbers have a 1 (everything else is 0).

  3          =>  00011
& 5          =>  00101
----           -------
1                00001

Bitwise OR

Take two numbers, line them up on top of each other, and create a new number that has a 1 where either number has a 1 (everything else is 0).

  3          =>  00011
| 5          =>  00101
----           -------
7                00111

Bitwise NOR (Not OR)

Take the Bitwise OR of two numbers, and then reverse everything (where there was a 0, there's now a 1, where there was a 1, there's now a 0)

# simplified gate view ^(3|5)

^
( 3           =>  00011
| 5)          =>  00101
----           -------
6                 11000 

Bitwise XOR (exclusive OR)

Take two numbers, line them up on top of each other, and create a new number that has a 1 where either number has a 1 AND the other number has a 0 (everything else is 0).

  3          =>  00011
^ 5          =>  00101
----           -------
6                00110 

Bitwise NAND (Not AND)

Take the Bitwise AND of two numbers, and then reverse everything (where there was a 0, there's now a 1, where there was a 1, there's now a 0).

    n          =>  abcdefghjikl
&   15         =>  000000001111
------            --------------
    ?              00000000jikl

Bitshift Operator

means "shift everything left n bits" or "shift everything right n bits"

1 << 3 = 0001 << 3 = 0001000 = 8

And:

8 >> 2 = 01000 >> 2 = 010 = 2

Truth table for all binary logical operators

Online Base Convertor