## What are Bitwise Operators in Python?

Bitwise operators in Python are used to perform operations on binary numbers, i.e., numbers represented in the base-2 number system. These operators aid in performing operations on data at the bit level, which helps provide valuable insights and optimise the performance of certain algorithms. Understanding these operators also comes in handy when you want to manipulate bits directly in applications such as embedded systems, cryptography, and computer graphics.

### Python Bitwise Operators Precedence

In Python, as in other programming languages, there is a hierarchy of precedence for operators. This indicates the order in which the operations are executed. As for bitwise operators, their precedence falls somewhere in the middle of the hierarchy. When an expression contains multiple operators with different precedence levels, the ones with higher precedence are performed before the others.

Here is the order of precedence for the bitwise operators in Python:

- Bitwise NOT: ~
- Bitwise shift: << and >>
- Bitwise AND: &
- Bitwise XOR: ^
- Bitwise OR: |

## Types of Python Bitwise Operators

There are several types of bitwise operators in Python, each performing a specific operation on binary numbers. Here is a list of the primary Python bitwise operators:

- Bitwise AND (&)
- Bitwise OR (|)
- Bitwise XOR (^)
- Bitwise NOT (~)
- Bitwise Left Shift (<
- Bitwise Right Shift (>>)

Each of these operators has a specific functionality:

Operator | Description |

& | Executes a 'Bitwise AND' operation on the corresponding bits of the provided binary numbers; a bit will be 1 only if the corresponding bits in both numbers are 1, otherwise, it is 0. |

| | Conducts a 'Bitwise OR' operation on the corresponding bits of the given binary numbers; a bit will be 1 if any of the corresponding bits in the two numbers is 1, otherwise, it is 0. |

^ | Carries out a 'Bitwise XOR' operation on the corresponding bits of the input binary numbers; a bit will be 1 if the corresponding bits in each number are different, otherwise, it is 0. |

~ | Operates as a 'Bitwise NOT' operator by inverting the bits of given binary numbers; a 0 bit becomes 1 and a 1 bit becomes 0. |

<< | Conducts a 'Bitwise Left Shift' operation, shifting the bits of the input binary number to the left by a certain number of positions, and filling the empty positions with 0 bits. |

>> | Executes a 'Bitwise Right Shift' operation, shifting the bits of the input binary number to the right by a certain number of positions and filling the empty positions with 0 bits. |

For example, let's assume two binary numbers: A = 1010 and B = 1100. Using the bitwise AND operator (&) on A and B would result in: A & B = 1000.

## Practical Applications of Python Bitwise Operators

Python bitwise operators might not be the most commonly used operators, but they have crucial applications in various computer science fields. They allow efficient manipulation of bits in data and are helpful for optimising performance and memory in certain areas such as binary arithmetic, cryptography, computer graphics, embedded systems, and network protocols.

### How to Use Bitwise Operators in Python

To effectively use Python bitwise operators, it is important to understand their functionality and apply them properly. These operators can be used directly in expressions, just like any other mathematical operators. Below, we provide step-by-step instructions for using Python bitwise operators along with some helpful tips:

- Identify which specific bitwise operation is required for the task at hand. Consult the table in the "Types of Python Bitwise Operators" section above for a brief overview of each operator.
- Convert the given numbers, if not already in binary format, to binary using the `bin()` function or any other Python technique.
- Apply the appropriate bitwise operator(s) on the binary numbers in an expression.
- If necessary, convert the result back to the desired number format such as decimal, hexadecimal or octal.
- Test your code to verify that the desired bitwise operation has been executed correctly. Ensure that your code handles edge cases and potential exceptions as well.

It is essential to note that bitwise operators work exclusively with integers in Python. Make sure the data type of the operands for the bitwise operation is `int`. If the data type is different, you need to convert it to an integer using the `int()` function before performing bitwise operations.

#### Python Bitwise Operators with Examples

Now that we have covered how to use bitwise operators in Python, let us examine some examples to gain a better understanding. In the following examples, we will use decimal numbers and convert them to binary numbers using the `bin()` function for a clear demonstration of the bitwise operations.

Example 1:Suppose we have two decimal numbers, A = 10 and B = 12:A in binary: \(1010_2\)B in binary: \(1100_2\)Let's apply the bitwise AND (&) operator:Result: \(1000_2\)This result in decimal form is 8.

Example 2:Let's use the same binary numbers for A and B as in the previous example.A in binary: \(1010_2\)B in binary: \(1100_2\)Now, apply the bitwise OR (|) operator:Result: \(1110_2\)The result in decimal form is 14.

Example 3:Again, we'll use the same binary numbers for A and B as in the previous examples.A in binary: \(1010_2\)B in binary: \(1100_2\)This time, apply the bitwise XOR (^) operator:Result: \(0110_2\)The result in decimal form is 6.

Example 4:Let's take A = 10 in binary form as the input number:A in binary: \(1010_2\)Apply the bitwise NOT (~) operator:Result: \(-1011_2\)The result in decimal form is -11.Note that the negative sign indicates two's complement representation.

These examples demonstrate the basic usage of Python bitwise operators. They can be combined and used in more complex expressions as required in various programming scenarios.

## Comparing Bitwise and Logical Operators

In Python, both bitwise and logical operators are used for different purposes and have distinct characteristics. Bitwise operators, as discussed before, perform operations directly on the bits of binary numbers. On the other hand, logical operators operate on Boolean values (True and False) and are used for making decisions in control flow statements like `if`, `while`, and `for`. Now, let's delve into these operators to better understand their applications and key differences.

### Key Differences Between Bitwise and Logical Operators

Here are some essential differences between bitwise and logical operators in Python:

**Operations on Bits vs Boolean Logic:**Bitwise operators execute operations on binary numbers' individual bits, whereas logical operators apply Boolean logic (AND, OR, NOT) on given conditions that yield True or False.**Operands:**Bitwise operators work specifically with integers as their operands, whereas logical operators can handle any Python objects that can be evaluated to a Boolean value.**Application:**Bitwise operators are most commonly applied in low-level programming tasks such as binary arithmetic, computer graphics, embedded systems, and cryptography. Logical operators, however, are widely used in various programming scenarios, ranging from simple conditional statements to complex decision-making tasks.**Syntax:**Bitwise operators use different syntax compared to their logical counterparts. For example, bitwise operators use symbols like &, |, ^, and ~, while logical operators use keywords like `and`, `or`, and `not`.

It is important to note that although the operations performed by bitwise and logical operators differ significantly, they share some similarities in syntax and concept. For example, both the bitwise AND operator (&) and the logical AND operator (`and`) require the corresponding elements to be 'True' (1 for bitwise and True for logical) to produce a 'True' value. Nevertheless, despite these similarities, the two sets of operators work on distinct data types and are employed for different purposes.

Additionally, here is a comparison table detailing the bitwise and logical operators in Python:

Category | Operators | Description |

Bitwise Operators | & | Bitwise AND |

| | Bitwise OR | |

^ | Bitwise XOR | |

~ | Bitwise NOT | |

<< | Bitwise Left Shift | |

>> | Bitwise Right Shift | |

Logical Operators | and | Logical AND |

or | Logical OR | |

not | Logical NOT |

In conclusion, understanding the key differences between Python's bitwise and logical operators is crucial for selecting the appropriate set of operators based on the requirements of the specific programming task at hand. Each operator set caters to different applications, and using them correctly improves the efficiency, readability, and functionality of your code.

## Python Bitwise Operators - Key takeaways

Python Bitwise Operators: Perform operations on binary numbers' individual bits.

Bitwise vs Logical Operators in Python: Bitwise operators work with integer operands; Logical operators work with Boolean values.

Python Bitwise Operators Precedence: ~, << and >>, &, ^, |.

Types of Python Bitwise Operators: AND (&), OR (|), XOR (^), NOT (~), Left Shift (<>).

Python Bitwise Operators with Examples: e.g. & operator: A = 1010, B = 1100, A & B = 1000.

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