This course teaches bit manipulation, a powerful technique to enhance algorithmic and problem-solving skills. It is a critical topic for those preparing for coding interviews for top tech companies, startups and industry leaders. Competitive programmers can take full advantage of this course by running most of the bit-related problems in O(1) complexity.

The course will begin by educating you about the number system and its representation, decimal and binary, followed by the six bitwise operators: AND, OR, NOT, XOR, and bit-shifting (left, right).

You will receive ample practical experience working through practice problems to improve your comprehension.

Upon completing this course, you will be able to solve problems with greater efficiency and speed.

Grokking Bit Manipulation for Coding Interviews

## Logical right shift (>>>)

The logical right shift operator is written as `>>>`.

Integers are stored in memory as a series of bits. 
For example, the number `12` stored as a 32-bit `int` would be:

```
12 = 00000000 00000000 00000000 00001100
```

When we shift it one position `(12 >>> 1)`, the answer is 6.

`12 >>> 1` = $\frac{12}{2^1}$ = $\frac{12}{2}$ = 6.

The binary representation of the number 6 is as follows.

```
(12 >>> 1) = 00000000 00000000 00000000 00000110
```

Let's see how to represent this in a mathematical formula.

### Formula

> a >>> b = $\frac{a}{2^b}$

# Logical right shift (>>>)

The logical right shift operator is written as `>>>`.

Integers are stored in memory as a series of bits. 
For example, the number `12` stored as a 32-bit `int` would be:

```
12 = 00000000 00000000 00000000 00001100
```

When we shift it one position `(12 >>> 1)`, the answer is 6.

`12 >>> 1` = $\frac{12}{2^1}$ = $\frac{12}{2}$ = 6.

The binary representation of the number 6 is as follows.

```
(12 >>> 1) = 00000000 00000000 00000000 00000110
```

Let's see how to represent this in a mathematical formula.

## Formula

> a >>> b = $\frac{a}{2^b}$

The logical right shift means shifting the bits to the right, and MSB(most significant bit) becomes 0. The arithmetic right shift means shifting the bits to the right, and MSB is the same as in the original number.

Getting Started

Number Systems, Bitwise, and Binary

Bitwise AND

Bitwise OR

Bitwise NOT

Bitwise XOR

Bit Shifting - Left, Right

Bitwise LeftShift Problems

Bitwise RightShift Problems

Final Thoughts

Arithmetic and Logical Right Shifts

Logical right shift (>>>)

Formula