Bitwise Operations

Why manipulate bits?

Bitwise operations allow manipulating binary values directly, that is, bit by bit. They are widely used in low-level computing, but also in concrete situations like:

Controlling options in an application (each bit representing a parameter)
Data compression and encryption
Processing images, sounds or signals
Microcontrollers and embedded systems

These operations are fast, memory-efficient, and often used in systems where resources are limited.

How does it work?

Each integer is represented by a sequence of bits (0 or 1). Bitwise operations compare or modify these bits individually.

Example:

# Binary representation
x = 5   # 0b0101
y = 3   # 0b0011

Main bitwise operations

Operation	Symbol	Effect	Example
Logical AND	`&`	1 if both bits are 1	`0b0101 & 0b0011 = 0b0001`
Logical OR	`\|`	1 if at least one of the two bits is 1	`0b0101 \| 0b0011 = 0b0111`
Exclusive OR (XOR)	`^`	1 if only one of the two bits is 1	`0b0101 ^ 0b0011 = 0b0110`
Logical NOT	`~`	Inverts all bits (two's complement)	`~0b00000000 = 0b11111111`
Left shift	`<<`	Shifts bits to the left (multiplies)	`0b00000001 << 1 = 0b00000010`
Right shift	`>>`	Shifts bits to the right (divides)	`0b00000100 >> 1 = 0b00000010`

Binary representation

An integer can be displayed in binary with the format(n, '08b') function, which displays the number on 8 bits. Example:

state = 0b00000110
print(format(state, '08b'))  # Displays 00000110

Concrete example: options stored in a byte

Suppose a program stores several options in a single byte. Each bit represents an activated (1) or deactivated (0) option.

Bit 0: Sound enabled
Bit 1: Bluetooth enabled
Bit 2: Wi-Fi enabled
Bit 3: Airplane mode enabled
Bit 4: Notifications enabled

Check if an option is activated

state = 0b00000110  # Wi-Fi and Bluetooth enabled
wifi = 0b00000100
if state & wifi:
    print("Wi-Fi enabled")

Activate an option (ex: airplane mode)

state |= 0b00001000  # Activates bit 3

Deactivate an option (ex: Bluetooth)

state &= ~0b00000010  # Sets bit 1 to 0

Toggle an option (XOR)

state ^= 0b00000100  # If Wi-Fi was enabled, it's disabled, and vice versa

Summary

Bitwise operations act directly on the binary representation of integers
They allow manipulating data in a fine, efficient and fast way
The most common operators are &, |, ^, ~, <<, >>
We can use bits to store and manage multiple states in a single integer variable

These concepts are useful in algorithms, electronics, and in all systems where memory optimization and execution speed are important.