# Find the right most unset bit OR zero bit of a number

**Objective: **Given a number, write and algorithm to find the right most unset bit or zero bit in it (In binary representation).

This problem is similar to: Find the right most set bit of a number

**Example:**

Number : 11 Binary representation: 1 0 1 1 Position of right most unset bit: 2 Number : 6 Binary representation: 1 1 0 Position of right most unset bit: 0 Number : 13 Binary representation: 1 1 0 1 Position of right most unset bit: 1

**Approach:**

If N is a number then the expression below will give the right most unset bit.

~N & (N +1)

- Let’s dig little deep to see how this expression will work.
- We know that N & ~N = 0
- If we add 1 from the number, it will make most unset bit to 1, if there are any set bits in the right side of unset bit, those bit will become zero.
- (example : 1 0 1 1 + 0 0 0 1 = 1 1 0 0)
- So if we negate the original number it will make the right most unset bit to 1.
- Now ~N & (N+1) will make all the bits 0 but the right most unset bit of a number.

**Example**:

Say N =11, so N = 1 0 1 1 N + 1 = 1 1 0 0 ~N = 0 1 0 1 ~N & (N+1) = 0 1 0 0 => 2^{nd}bit (assuming right most index is 0)

**Code**:

**Output**:

Right most Unset bit :2.0

In example ~N = 0 1 0 1 should be 0100