Bitwise Operations

Bitwise Operators in C

The bitwise operators in c for and, or, not and exclusive are &, |, ~, and ^ respectively. That is, if we apply these to any primitive data type, the bit-level representation of the two operands will be operated on.

Example: NOT

Assume we have the variables x=0x41 and y=0xBE. Note that each is 1 byte in size (2 hex digits). Since they are only 1 byte, let’s say they represent a char.

Performing ~x:

// Given
~x             

// Represent the value as it was given in hex.
~0x41        

// Note that the hex value 4 is 0100 in binary and the hex value of 1 is 0001 in binary.
// We can represent them together as the following:
// Note that the space is only included for visual purposes here.
~0100 0001    

// Now we apply the negation and flip every bit.           
 1011 1110

// Representing this back in it's hex form gives the following.
// The bits 1011 are the hex value B and the bits 1110 are the hex value E.
 0xBE   // The final result after negation and as a hex value.

Example: AND

Find the result (in hex) of simplifying the expression x & y when x = 0x69 and y = 0x55

Solution:

        Binary     Hex

      01101001    0x69     // Value 1
    & 01010101    0x55     // Value 2
    ----------   -----
      01000001    0x41     // Result

Example: AND and NOT

Find the result (in hex) of simplifying the expression ~(x & y) when x = 0xb4 and y = 0x87

Solution:

        Binary     Hex
      10110100    0xb4      // x
   &  10000111    0x87      // y
   -----------   -----
      10000100    0x84      // Intermediate result (x & y)

     ~10000100    0x84      // Apply ~
   -----------   -----
      01111011    0x7B      // Final result ~(x & y)

Example: OR

Find the result (in hex) of simplifying the expression x | y when x = 0x69 and y = 0x55.

Solution:

        Binary     Hex

      01101001    0x69     // Value 1
    | 01010101    0x55     // Value 2
    ----------   -----
      01111101    0x7D     // Result   

Example: OR

Find the result (in hex) of simplifying the expression x | y when x = 0xb4 and y = 0x87.

Solution:

        Binary     Hex

      10110100    0xb4
    | 10000111    0x87
    ----------   -----
      10110111    0xB7

Example: NOT, OR, and AND

Find the result (in hex) of simplifying the expression x | ~(y & z) when x = 0xA7, y = 0x8, and z = 0x5.

Solution:

        Binary     Hex

    // Get the intermediate result (y & z)
        Binary     Hex
          1000     0x8   // y
    &     0101     0x5   // z
    ----------   -----
          0000     0x0   // (y & z)


    // Get the intermediate result ~(y & z)
        Binary     Hex
    ~     0000     0x0   // (y & z)
    ----------   -----
          1111     0xF   // ~(y & z)

    // Get the final result
        Binary     Hex
      10100111    0xA7   // x
    | 00001111    0x0F   // ~(y & z)
    ----------   -----
      10101111    0xAF   // Final Result x | ~(y & z)