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⚙️ C++ Bitwise Operators – Manipulate Data at the Binary Level

🧲 Introduction – What Are Bitwise Operators in C++?

Bitwise operators in C++ perform operations directly on the binary representation of integers. They are powerful tools for low-level programming, including embedded systems, performance optimization, and hardware-level applications.

🎯 In this guide, you’ll learn:

The list and purpose of bitwise operators
Syntax and usage examples
Bitwise shift operations
Common tricks and real-world applications

🧮 List of C++ Bitwise Operators

Operator	Symbol	Description	Example	Result (Binary)
AND	`&`	Sets bits that are 1 in both	`a & b`	`0000 0100`
OR	`	`	Sets bits that are 1 in either	`a
XOR	`^`	Sets bits that differ	`a ^ b`	`0000 1010`
NOT	`~`	Inverts all bits	`~a`	Complemented
Left Shift	`<<`	Shifts bits left (multiplies)	`a << 1`	`0001 0000`
Right Shift	`>>`	Shifts bits right (divides)	`a >> 1`	`0000 0010`

Example values:
int a = 12; // 0000 1100
int b = 10; // 0000 1010

✅ Example – Bitwise Operators in Action

#include <iostream>
using namespace std;

int main() {
    int a = 12, b = 10;

    cout << "a & b = " << (a & b) << endl;
    cout << "a | b = " << (a | b) << endl;
    cout << "a ^ b = " << (a ^ b) << endl;
    cout << "~a = " << (~a) << endl;
    cout << "a << 1 = " << (a << 1) << endl;
    cout << "a >> 1 = " << (a >> 1) << endl;

    return 0;
}

🧠 Binary Representation Visual

Decimal	Binary
12	`00001100`
10	`00001010`

AND (12 & 10): 00001000 = 8
OR  (12 | 10): 00001110 = 14
XOR (12 ^ 10): 00000110 = 6

📦 Bit Shifting Explained

🔁 Left Shift `<<`

int x = 5;           // 00000101
int result = x << 1; // 00001010 = 10

✅ Effectively multiplies by 2

🔁 Right Shift `>>`

int y = 8;           // 00001000
int result = y >> 1; // 00000100 = 4

✅ Effectively divides by 2

⚠️ Common Mistakes

❌ Mistake	✅ Fix
Using bitwise operators on floats	Bitwise ops work only with integers
Ignoring sign with right shift	Use unsigned types to avoid sign-extension surprises
Confusing `&` with `&&`	`&` is bitwise AND; `&&` is logical AND

🧠 Real-World Uses of Bitwise Operators

Masking specific bits int mask = 0x0F; // 00001111 result = value & mask;
Checking parity (even/odd) if (num & 1) cout << "Odd";
Fast multiplication/division by powers of 2
Permissions (bit flags in enums)

📌 Summary – Recap & Next Steps

🔍 Key Takeaways:

Bitwise operators allow direct manipulation of bits
Use &, |, ^, ~ for basic binary operations
Use << and >> for shifting (efficient multiplication/division)
Ideal for performance-critical and embedded programming

⚙️ Real-World Relevance:
Bitwise operations power digital systems, graphics engines, compression algorithms, and microcontroller code.

❓ FAQs – C++ Bitwise Operators

❓ Can bitwise operators be used with float or double?
❌ No. Use only with integers or cast to integer first.

❓ What does a << 1 do?
✅ Shifts all bits of a one position left — effectively a * 2.

❓ What is the difference between & and &&?
✅ & is bitwise AND; && is logical AND.

❓ How do I set, clear, or toggle a bit?
✅ Use masks:

Set: num |= (1 << i)
Clear: num &= ~(1 << i)
Toggle: num ^= (1 << i)

❓ Is ~a the same as -a?
❌ No. ~a inverts all bits. -a is two’s complement negation.

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