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What is Bit Manipulation?

Bit manipulation refers to the process of directly handling individual bits of a number using bitwise operations. It is a crucial concept in computing, optimizing performance in tasks like encryption, compression, and low-level programming.

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Why is Bit Manipulation Important?

  • Fast Operations: Bitwise operations are much faster than arithmetic operations.
  • Memory Efficiency: Used in data compression and storage optimization.
  • Low-Level System Programming: Essential for working with hardware, microcontrollers, and embedded systems.
  • Algorithm Optimization: Used in fast calculations, cryptography, and data structures like bitsets and Bloom filters.

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Bitwise Operators

Bit manipulation primarily involves six operators:

OperatorSymbolDescription
AND&Sets a bit if both corresponding bits are 1
OR`Sets a bit if at least one corresponding bit is 1
XOR^Sets a bit if only one corresponding bit is 1
NOT~Inverts all bits (bitwise complement)
Left Shift<<Shifts bits to the left, multiplying by 2^n
Right Shift>>Shifts bits to the right, dividing by 2^n

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1. Bitwise AND (&)

let a = 5; // 0101 (binary)
let b = 3; // 0011 (binary)
console.log(a & b); // 0001 (1 in decimal)

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2. Bitwise OR (|)

let a = 5; // 0101
let b = 3; // 0011
console.log(a | b); // 0111 (7 in decimal)

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3. Bitwise XOR (^)

let a = 5; // 0101
let b = 3; // 0011
console.log(a ^ b); // 0110 (6 in decimal)

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4. Bitwise NOT (~)

let a = 5; // 00000101 (8-bit representation)
console.log(~a); // 11111010 (-6 in decimal due to two's complement)

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5. Left Shift (<<)

let a = 5; // 0101
console.log(a << 1); // 1010 (10 in decimal)

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6. Right Shift (>>)

let a = 5; // 0101
console.log(a >> 1); // 0010 (2 in decimal)

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Common Bit Manipulation Tricks

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1. Checking if a Number is Even or Odd

function isEven(n) {
  return (n & 1) === 0;
}

console.log(isEven(4)); // true
console.log(isEven(7)); // false

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2. Checking if a Number is a Power of 2

function isPowerOfTwo(n) {
  return n > 0 && (n & (n - 1)) === 0;
}

console.log(isPowerOfTwo(8)); // true
console.log(isPowerOfTwo(10)); // false

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3. Swapping Two Numbers Without a Temporary Variable

let x = 5,
  y = 3;
x = x ^ y;
y = x ^ y;
x = x ^ y;
console.log(x, y); // 3, 5

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4. Counting Set Bits in a Number (Brian Kernighan’s Algorithm)

function countSetBits(n) {
  let count = 0;
  while (n > 0) {
    n &= n - 1;
    count++;
  }
  return count;
}

console.log(countSetBits(9)); // 2 (1001 has 2 set bits)

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Applications of Bit Manipulation

  • Data Compression (Huffman Encoding)
  • Cryptography (Encryption & Decryption)
  • Graphics Rendering (Efficient pixel manipulation)
  • Networking (Bit masking in IP addressing)
  • Embedded Systems (Working with hardware registers)

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Summary

Bit manipulation is a powerful tool in computing, enabling efficient data processing, fast algorithms, and low-level programming. Mastering bitwise operations can significantly improve your problem-solving skills in competitive programming, system programming, and embedded development.