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Bit Manipulation

🔢 Bit Manipulation

Section titled “🔢 Bit Manipulation”

Welcome to the Bit Manipulation section. This module covers everything from reading binary numbers to advanced bitmask techniques that appear in competitive programming and technical interviews.

🧠 Why Bit Manipulation Matters

Section titled “🧠 Why Bit Manipulation Matters”

Bit manipulation is one of those topics that separates candidates who “know DSA” from candidates who truly understand how computers work. Interviewers at FAANG and top-tier companies regularly ask bit manipulation problems because they test:

  • Low-level thinking — do you understand how data is stored?
  • Optimization instinct — can you replace expensive operations with O(1) bit tricks?
  • Pattern recognition — XOR patterns, bitmask DP, subset enumeration
Speed comparison for common operations:
  n % 2 === 0   (mod)    → check even/odd   [slower]
  (n & 1) === 0 (bit)    → check even/odd   [faster, O(1) at hardware level]


  Math.floor(n / 2)      → divide by 2      [slower]
  n >> 1                 → divide by 2      [single CPU instruction]

📖 Topics Covered

Section titled “📖 Topics Covered”

🎯 Foundations

Section titled “🎯 Foundations”
  • Introduction — Binary representation, two’s complement, all 6 bitwise operators with truth tables
  • Bit Tricks — 15+ essential tricks: check even/odd, power of two, get/set/clear/toggle bits, Brian Kernighan’s algorithm

💡 Patterns

Section titled “💡 Patterns”
  • XOR Patterns — The XOR identity laws and 7 classic XOR-based problem patterns

🧩 Problem Solving

Section titled “🧩 Problem Solving”
  • Practice Problems — 10 fully solved problems: Hamming Weight, Reverse Bits, Counting Bits, Gray Code, UTF-8 Validation, and more
  • Interview Questions — 12+ Q&A covering every trick an interviewer is likely to ask

📚 Recommended Learning Path

Section titled “📚 Recommended Learning Path”
StepFocusTopic
1UnderstandStart with Introduction — learn the operators
2Memorize TricksStudy Bit Tricks — these recur constantly
3Master XORRead XOR Patterns — XOR is the most interview-tested operator
4Solve ProblemsWork through Practice Problems one by one
5Interview PrepDrill Interview Questions until answers are instant

⚡ Quick Reference Card

Section titled “⚡ Quick Reference Card”
OPERATOR   SYMBOL   EXAMPLE         RESULT   USE CASE
AND          &       5 & 3           1        Mask / check bits
OR           |       5 | 3           7        Set bits
XOR          ^       5 ^ 3           6        Toggle / find unique
NOT          ~       ~5             -6        Complement
Left Shift   <<      5 << 1         10        Multiply by 2ⁿ
Right Shift  >>      5 >> 1          2        Divide by 2ⁿ (signed)
Unsigned >>  >>>     -1 >>> 0  4294967295     Treat as unsigned 32-bit

🔥 Top Interview Tricks at a Glance

Section titled “🔥 Top Interview Tricks at a Glance”
TrickCode
Is odd?n & 1
Is power of two?n > 0 && (n & (n-1)) === 0
Get i-th bit(n >> i) & 1
Set i-th bitn | (1 << i)
Clear i-th bitn & ~(1 << i)
Toggle i-th bitn ^ (1 << i)
Clear lowest set bitn & (n - 1)
Isolate lowest set bitn & (-n)
Count set bitsBrian Kernighan’s algorithm
Swap without tempa ^= b; b ^= a; a ^= b

🔗 Related Topics

Section titled “🔗 Related Topics”
  • Recursion & Backtracking — Subset enumeration via bitmask pairs well with recursive subset generation
  • Arrays — Many bitmask tricks apply directly to array problems
  • Dynamic Programming — Bitmask DP is a powerful technique for state compression