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

>>> 5 << 1
10

Divide a number by 2

>>> 6 >> 1
3

Multiply by mth power of 2

>>> n = 5
>>> n << 3
40

Divide by mth power of 2

>>> n = 40
>>> n >> 3
5

Exchange two values

>>> x = 3
>>> y = 5

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

>>> x
5
>>> y
3

Check if an integer is even or odd

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

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

Check Equality of two numbers

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

Check if a number is a power of two

>>> 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:

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

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

>>> 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

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

Convert integer to binary number

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

Resources

• awesome-bits
• A Bit of Fun: Fun with Bits - Topcoder
• Bit Manipulation - HackerEarth
• Bit Twiddling Hacks - Stanford