As we discussed in the previous video, the numbers are stored in their binary representation in computers and every single digit 0 / 1 is called bit.
Most languages allow you to perform operations which are bitwise ( this statement will make much more sense when we look at the operator themselves ). It is a fast, primitive action directly supported by the processor, and is used to manipulate values for comparisons and calculations.

• Bitwise &
• Bitwise |
• Bitwise XOR
• Bitwise NOT
• Right shift operator
• Left Shift Operator

Syntax:

A & B

Values for bit combinations:

            a      b         a & b 
           ------------------------
            0      0         0
            0      1         0
            1      0         0
            1      1         1

In other words, a & b = 0 unless a = 1 and b = 1.

What does A & B mean:

A & B implies a & b for all corresponding bits of A and B.

So, lets say,

       A = 21 ( 10101 ) and B = 6  ( 110 ) 
       A & B = 
                        1 0 1 0 1
                    &   0 0 1 1 0  
                    ------------------
                        0 0 1 0 0  =  4. 

Syntax :

A | B

Values for bit combinations

            a      b      a | b 
           ------------------------
            0      0         0
            0      1         1
            1      0         1
            1      1         1

In other words, a | b = 1 unless a = 0 and b = 0

What does A | B mean :

A | B implies a | b for all corresponding bits of A and B. So, lets say

       A = 21 ( 10101 ) and B = 6  ( 110 ) 
       A | B = 
                        1 0 1 0 1
                    |   0 0 1 1 0  
                    ------------------
                        1 0 1 1 1  =  23. 

Syntax :

A ^ B

Values for bit a, b :

            a      b      a ^ b 
          ------------------------
            0      0         0
            0      1         1
            1      0         1
            1      1         0

In other words, a ^ b = 1 when a and b are different.

What does A ^ B mean :

A ^ B implies a ^ b for all corresponding bits of A and B. So, lets say

       A = 21 ( 10101 ) and B = 6  ( 110 ) 
       A ^ B = 
                        1 0 1 0 1
                    ^   0 0 1 1 0  
                    ------------------
                        1 0 0 1 1  =  19. 

Syntax :

~A

Values for bit a :

                                a   |   ~a
                             -------|-------
                                0   |   1
                                1   |   0

It's the inverse of the bit.

What does ~A mean

~A implies inverting every single bit in A. So, lets say

            A = 21 ( 10101 ) and A is a char ( 1 byte )

            ~A = 

                0 0 0 1 0 1 0 1

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

                1 1 1 0 1 0 1 0  = -22 ( Sign bit is 1 ). 

Syntax :

A >> x

What does A » x mean :

A >> x implies shifting the bits of A to the right by x positions. The last x bits are lost this way.

Example : Lets say

                A = 29 ( 11101 ) and x = 2, 
                so A >> 2 means
                     0 0 1 1 1 0 1 >> 2
                               ====  -> is lost 
                    ========== -----> this sequence of digit shifts to the right by 2 positions
                    ----------------
                     0 0 0 0 1 1 1 = 7

A >> x is equal to division by pow(2, x). Think why.

Syntax :

A << x

What does A « x mean :

A << x implies shifting the bits of A to the left by x positions. The first x bits are lost this way. The last x bits have 0. Example : lets say

                A = 29 ( 11101 ) and x = 2, 
                so A << 2 means
                     0 0 1 1 1 0 1 << 2
                     =============  ------> this sequence of digit shifts to the left by 2 positions
                    ----------------
                     1 1 1 0 1 0 0  = 116 

A << x is equal to multiplication by pow(2, x). Think why. 1 << x is equal to pow(2, x).