Python Bitwise AND and OR Operators

Bitwise operators are similar to logical operators, but instead of operating on boolean values, they apply the same logic to all the bits in a value by column. The two operators covered here are & (AND) and | (OR).

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Binary Numbers in Python

Binary numbers are just "base 2" numbers. They work the same way as "normal" base 10 numbers, but with two symbols instead of ten.

• Base-2 (binary) symbols: 0 and 1
• Base-10 (decimal) symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Each digit's place value is double the place to its right. In a 4-digit binary number, the place values are:

• Eights
• Fours
• Twos
• Ones

For example, 0101 means:

• 0 eights
• 1 four
• 0 twos
• 1 one

So 0101 is 5 in decimal.

Try changing the bits:

You can write an integer in Python using binary syntax using the 0b prefix:

print(0b0001)
# Prints 1

print(0b0101)
# Prints 5

Leading 0s are often added for visual consistency but do not change the value of a binary number.

Bitwise AND (&)

Say you had the numbers 5 and 7 represented in binary. You could perform a bitwise AND operation and the result would be 5.

• 0101 is 5
• 0111 is 7

0101
&
0111
=
0101

A 1 in binary is the same as True, while 0 is False. So really a bitwise operation is just a bunch of logical operations that are completed in tandem by column.

Ampersand & is the bitwise AND operator in Python. "AND" is the name of the bitwise operation, while ampersand & is the symbol for that operation. For example, 5 & 7 = 5, while 5 & 2 = 0.

binary_five = 0b0101
binary_seven = 0b0111
print(binary_five & binary_seven)
# 5

Bitwise OR (|)

The bitwise "or" operator is similar to the bitwise "and" operator in that it works on binary rather than boolean values. However, the bitwise "or" operator "or"s the bits together.

0101
|
0111
=
0111

When two binary numbers are "or"ed together, the result has a 1 in any place where either of the input numbers has a 1 in that place.

| is the bitwise "or" operator in Python. 5 | 7 = 7 and 5 | 2 = 7 as well!

Using Bitwise Operators for Permissions

Sometimes applications store user permissions as binary values. If you have 4 different permissions a user can have, then you can store that as a 4-digit binary number, and if a certain bit is present, you know the permission is enabled. This can be a lot more efficient than storing entire strings.

can_read = 0b100
can_write = 0b010
can_execute = 0b001

user_perms = can_read | can_write  # 0b110
has_read = user_perms & can_read   # 0b100 (truthy — has permission)

Use bitwise AND to check whether a specific permission is enabled. Use bitwise OR to combine permissions.

Convert a Binary String to an Integer

The built-in int() function can convert a binary string to an integer. It takes a second argument that specifies the base of the number (binary is base 2). For example:

# this is a binary string
binary_string = "100"

# convert binary string to integer
num = int(binary_string, 2)
print(num)
# 4

If you're curious about how other bitwise operations show up in the real world, read why XOR is important in cryptography.