Computers don't see numbers like 42; they see electrical pulses: 101010. Bit manipulation is using the foundational operators of logic to solve problems with extreme speed and zero memory.

Think of a row of Light Switches:

1. Every number is just a sequence of ON (1) and OFF (0) switches.
2. AND (&): Both switches must be ON for the result to be ON.
3. OR (|): If at least one switch is ON, the result is ON.
4. XOR (^): If for two switches, exactly one is ON, the result is ON. (This is like a "Flip" operation).
5. NOT (~): Flips every switch.

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The 4 Operators you MUST know

• AND (&): 5 & 3 (101 & 011) = 001 (1). Useful for checking if a bit is set.
• OR (|): 5 | 3 (101 | 011) = 111 (7). Useful for setting a bit.
• XOR (^): 5 ^ 3 (101 ^ 011) = 110 (6). Legendary Property: A ^ A = 0. Useful for finding unique elements.
• Shift (<<, >>): Moving bits left or right. Left shift by 1 is the same as multiplying by 2.

Common Tricks

• Check if even: (n & 1) === 0
• Check if power of 2: (n > 0) && (n & (n - 1)) === 0
• Toggle i-th bit: n ^ (1 << i)
• Clear i-th bit: n & ~(1 << i)

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One of the most famous bit manipulation interview questions.

javascript Standard
/**
 * Find the number that appears only once in an array where every other number appears twice.
 * Logic: XORing a number with itself results in 0. (A ^ A = 0)
 * Logic: XORing with 0 results in the number itself. (A ^ 0 = A)
 */
function singleNumber(nums) {
  let result = 0;
  for (let num of nums) {
    result ^= num;
  }
  return result;
}

// Example
const arr = [4, 1, 2, 1, 2];
console.log(singleNumber(arr)); // Output: 4

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Binary representation of negative numbers

Research Two's Complement. It's the standard way computers store signed integers. To get a negative number's binary: take the positive binary, flip all bits, and add 1.

Top Questions

• Count set bits (Hamming Weight).
• Reverse bits of a 32-bit integer.
• Bitwise AND of numbers range.
• Divide two integers without using multiplication/division. 🔌