While learning about XORs during a basic crypto class, I decided to take a side track and learn about a term that was always shrouded in mystery -- bitwise operators. As always, I wrote these as my own notes for later reference but I'm publishing them here in case they help other people. Happy to accept pull requests for corrections.

Bitwise Operators.md

(A bit of a tangent from crypto 101)

Bits and bytes

• Core contepts:

  • Bitwise operators work on bits.
  • Bits are used to express data in binary form.
  • Bits can have a value of either 1 (ie TRUE) or 0 (ie FALSE).

• Higher-level language constructs like floats and strings can all be represented as a series of bytes

  • 1 byte = 8 bits
    • ie 1100 1001
    • Each bit has two states (TRUE or FALSE) and there are 8 bites per byte
  • 2 ^ 8 = 256
    • two possible states for each bit, eight bits combined together
    • each byte can contain 256 possible values (between 0-255)
    • data structures that can take more than 256 values need to be stored using multiple bytes

Bitwise Operators

• Bitwise Operators operate on the binary representation of their inputs

  • That’s why sometimes the results of the operations don’t seem to make any sense to a human
  • examples below

• When you apply a bitwise operator on two inputs

  • it lines up each of the bits contained in the inputs’ bytes and compares them using the chosen bitwise operator
  • the comparison goes down the line, comparing each set of two bits and returning the result

Operators:

• AND — returns TRUE (1) if both bits are the same
• OR — returns TRUE (1) if either bit is TRUE (1)
• XOR — returns TRUE (1) if only one of the bits is TRUE (1) or FALSE (0) if they’re the same
• NOT — returns TRUE (1) if its input is FALSE (0) [only takes one input?]

Examples from stackoverflow:

201 AND 15:

        201: 1100 1001
    AND  15: 0000 1111
    ------------------
    IS   9  0000 1001

10 OR 12:

    10 | 12
    
    1010 #decimal 10
    1100 #decimal 12
    
    1110 #result = 14

Make sense? See also for more examples.