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:zero: :one: A collection of bit manipulation techniques.

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# Bit Hacks

A collection of bit manipulation techniques.

*The examples are done in Python but should work with most languages
 with hardly any modification.*

## Multiply a number by 2

```python
>>> 5 << 1
10

```

## Divide a number by 2

```python
>>> 6 >> 1
3

```

## Multiply by mth power of 2

```python
>>> n = 5
>>> n << 3
40

```

## Divide by mth power of 2

```python
>>> n = 40
>>> n >> 3
5

```

## Exchange two values

```python
>>> x = 3
>>> y = 5

>>> x ^= y
>>> y ^= x
>>> x ^= y

>>> x
5
>>> y
3

```

## Check if an integer is even or odd

```python
>>> n = 6
>>> n & 1 == 0
True

>>> n = 5
>>> n & 1 == 0
False

```

## Check Equality of two numbers

```python
>>> x = 42
>>> y = 42
>>> not x ^ y
True

```

## Check if a number is a power of two

```python
>>> n = 8
>>> n & (n-1) == 0
True

>>> n = 6
>>> n & (n-1) == 0
False

```

Note that 0 is incorrectly considered a power of 2 here. To remedy this, use:

```python
>>> n = 8
>>> n and not (n & (n - 1))
True

```

## Check whether the n-th bit is set of an integer

```python
>>> n = 5
>>> n & (1 << 2) > 0 # 2nd bit is set in 101 (zero-indexed).
True

>>> n = 2
>>> n & (1 << 2) > 0 # 2nd bit is not set 010
False

```

## Minimum and Maximum of two numbers

```python
>>> x = 5
>>> y = 2
>>> y ^ ((x ^ y) & -(x < y)) # minimum
2
>>> x ^ ((x ^ y) & -(x < y)) # maximum
5

```

## Convert integer to binary number

```python
>>> def binary(s):
...     return str(s) if s <= 1 else binary(s >> 1) + str(s & 1)
>>> binary(28)
'11100'

```

## Resources

* [awesome-bits](https://github.com/keon/awesome-bits)
* [A Bit of Fun: Fun with Bits - Topcoder](https://www.topcoder.com/community/data-science/data-science-tutorials/a-bit-of-fun-fun-with-bits/)
* [Bit Manipulation - HackerEarth](https://www.hackerearth.com/practice/notes/bit-manipulation/)
* [Bit Twiddling Hacks - Stanford](https://graphics.stanford.edu/~seander/bithacks.html)

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