WTF is bitwise ✨

$$$$ \begin{array}{|c|c|c|c|} \hline 2^x & \text{Value} & \text{Binary Form} & \text{Shift} \\ \hline 2^0 & 1 & 0001 & 1 \ll 0 \\ 2^1 & 2 & 0010 & 1 \ll 1 \\ 2^2 & 4 & 0100 & 1 \ll 2 \\ 2^3 & 8 & 1000 & 1 \ll 3 \\ 2^4 & 16 & 0001 0000 & 1 \ll 4 \\ 2^5 & 32 & 0010 0000 & 1 \ll 5 \\ 2^6 & 64 & 0100 0000 & 1 \ll 6 \\ \hline \end{array} $$

$$

Simple trick is : number of zeroes after 1 in binary form is equal to power of 2. For eg: if 2^3 = 8 then its binary form would be 1000(1 and 3 zeroes) and also 1 << 3.

1. if you want to multiply any 'n' number by 2, then n << 1

2. if you want to divide any 'n' number by 2, then n >> 1

3. if you want to multiply any 'n' number by 2^x, then n << x

4. if you want to divide any 'n' number by 2^x, then n >> x

5. Checking if a number is even or odd:

   • An integer n is even if (n & 1) == 0 and odd if (n & 1) == 1.

6. Swapping two numbers without using a temporary variable:

   •   a ^= b;
       b ^= a;
       a ^= b;
     

7. Setting a particular bit to 1:

   • To set the i-th bit of a number n to 1: n |= (1 << i).

8. Setting a particular bit to 0:

   • To set the i-th bit of a number n to 0: n &= ~(1 << i).

9. Toggling a particular bit:

   • To toggle the i-th bit of a number n: n ^= (1 << i).

10. Checking if a number is a power of two:

    • A number is a power of two if n & (n - 1) == 0 and n > 0.

11. Counting set bits (number of 1s) in a binary representation:

    •   int countSetBits(int n) {
            int count = 0;
            while (n) {
                n &= (n - 1);
                count++;
            }
            return count;
        }
      

12. Finding the rightmost set bit:

    • To find the position of the rightmost set bit (least significant bit), you can use n & -n.

13. Turning off the rightmost set bit:

    • To turn off the rightmost set bit: n &= (n - 1).

14. Extracting the rightmost set bit:

    • To extract the rightmost set bit: rightmostBit = n & -n.

15. Setting all bits in a number to 1:

    • To set all bits in a number to 1: n = (1 << numberOfBits) - 1.