Bitwise operation and usage

Question

Consider this code:

x = 1        # 0001
x << 2       # Shift left 2 bits: 0100
# Result: 4

x | 2        # Bitwise OR: 0011
# Result: 3

x & 1              


        

Answer 1

I hope this clarifies those two:

x | 2

0001 //x
0010 //2

0011 //result = 3

---

x & 1

0001 //x
0001 //1

0001 //result = 1

Answer 2

Bit representations of integers are often used in scientific computing to represent arrays of true-false information because a bitwise operation is much faster than iterating through an array of booleans. (Higher level languages may use the idea of a bit array.)

A nice and fairly simple example of this is the general solution to the game of Nim. Take a look at the Python code on the Wikipedia page. It makes heavy use of bitwise exclusive or, ^.

Answer 3

the following bitwise operators: &, |, ^, and ~ return values (based on their input) in the same way logic gates affect signals. You could use them to emulate circuits.

Answer 4

what are bitwise operators actually used for? I'd appreciate some examples.

One of the most common uses of bitwise operations is for parsing hexadecimal colours.

For example, here's a Python function that accepts a String like #FF09BE and returns a tuple of its Red, Green and Blue values.

def hexToRgb(value):
    # Convert string to hexadecimal number (base 16)
    num = (int(value.lstrip("#"), 16))

    # Shift 16 bits to the right, and then binary AND to obtain 8 bits representing red
    r = ((num >> 16) & 0xFF)

    # Shift 8 bits to the right, and then binary AND to obtain 8 bits representing green
    g = ((num >> 8) & 0xFF)

    # Simply binary AND to obtain 8 bits representing blue
    b = (num & 0xFF)
    return (r, g, b)

I know that there are more efficient ways to acheive this, but I believe that this is a really concise example illustrating both shifts and bitwise boolean operations.