Bitwise Operations

Besides the normal numeric operations (addition, subtraction, and so on), Python supports most of the numeric expressions available in the C language. This includes operators that treat integers as strings of binary bits. For instance, here it is at work performing bitwise shift and Boolean operations:

>>> x = 1               # 0001
>>> x << 2              # Shift left 2 bits: 0100
4
>>> x | 2               # Bitwise OR: 0011
3
>>> x & 1               # Bitwise AND: 0001
1

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In the first expression, a binary 1 (in base 2, 0001) is shifted left two slots to create a binary 4 (0100). The last two operations perform a binary OR (0001|0010 = 0011) and a binary AND (0001&0001 = 0001). Such bit-masking operations allow us to encode multiple flags and other values within a single integer.

This is one area where the binary and hexadecimal number support in Python 2.6 and 3.0 become especially useful—they allow us to code and inspect numbers by bit-strings:

>>> X = 0b0001          # Binary literals
>>> X << 2              # Shift left
4
>>> bin(X << 2)         # Binary digits string
'0b100'

>>> bin(X | 0b010)      # Bitwise OR
'0b11'
>>> bin(X & 0b1)        # Bitwise AND
'0b1'

>>> X = 0xFF            # Hex literals
>>> bin(X)
'0b11111111'
>>> X ^ 0b10101010      # Bitwise XOR
85
>>> bin(X ^ 0b10101010)
'0b1010101'

>>> int('1010101', 2)   # String to int per base
85
>>> hex(85)             # Hex digit string
'0x55'

We won’t go into much more detail on “bit-twiddling” here. It’s supported if you need it, and it comes in handy if your Python code must deal with things like network packets or packed binary data produced by a C program. Be aware, though, that bitwise operations are often not as important in a high-level language such as Python as they are in a low-level language such as C. As a rule of thumb, if you find yourself wanting to flip bits in Python, you should think about which language you’re really coding. In general, there are often better ways to encode information in Python than bit strings.

Note

In the upcoming Python 3.1 release, the integer bit_length method also allows you to query the number of bits required to represent a number’s value in binary. The same effect can often be achieved by subtracting 2 from the length of the bin string using the len built-in function we met in Chapter 4, though it may be less efficient:

>>> X = 99
>>> bin(X), X.bit_length()
('0b1100011', 7)
>>> bin(256), (256).bit_length()
('0b100000000', 9)
>>> len(bin(256)) - 2
9