Bit Manipulation Algorithms

Computers use bits. A bit is a 0 or 1. All data is stored as bits.

Bit manipulation means changing or checking bits using special operations.

These operations are fast and powerful.

1. Why Learn Bit Tricks?

• They make your code faster.
• They are useful in games, compression, and graphics.
• They help solve coding problems in interviews.

2. Daily Life Analogy

Think of a bit as a light switch. 0 means off, 1 means on.

You can turn it on, turn it off, or flip it.

Just like you control lights in a room.

3. Common Bit Operators

Note: 5 in binary = 101, 3 = 011

4. Set a Bit

Turn a bit ON at a position.

int n = 5; // 0101
int pos = 1;
n = n | (1 << pos); // sets bit at pos
  

New value = 7 (0111)

5. Clear a Bit

Turn a bit OFF at a position.

int n = 5; // 0101
int pos = 2;
n = n & ~(1 << pos);
  

New value = 1 (0001)

6. Toggle a Bit

Flip a bit at a position.

int n = 5; // 0101
int pos = 0;
n = n ^ (1 << pos); // toggle bit
  

New value = 4 (0100)

7. Check if Bit is Set

See if a bit is ON.

int n = 5;
int pos = 2;
bool isSet = (n & (1 << pos)) != 0;
  

True, because bit 2 is ON in 101

8. Count Set Bits

How many 1s in the number?

int count = 0;
int n = 13; // 1101
while (n != 0) {
  count += n & 1;
  n = n >> 1;
}
  

Answer = 3

9. Is Number Power of Two?

Only one bit is set in power of 2.

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

8 → 1000, 7 → 0111 → AND = 0 → true

10. Swap Numbers Without Temp

int a = 5, b = 7;
a = a ^ b;
b = a ^ b;
a = a ^ b;
  

a = 7, b = 5 (Swapped!)

11. Applications in Real Life

• Games: control game states using bits.
• Compression: pack many settings into one number.
• Networks: encode and decode messages.
• Cryptography: secure data using bit operations.

Summary

• Bits are 0 and 1. They are fast to work with.
• Use AND, OR, XOR, shifts to manipulate bits.
• Helpful in many coding problems and systems.
• Daily tasks like light switches work like bits!

Fun Fact

A 32-bit number can store 32 yes/no answers. You can track 32 settings using just 1 number!