Two's Complement in Python

Question

Is there a built in function in python which will convert a binary string, for example '111111111111', to the two's complement integer -1?

Answer 1

But '111111111111' as an integer is 4095. What did you actually mean?

You could always

int('111111111111',2)

Answer 2

A couple of implementations (just an illustration, not intended for use):

def to_int(bin):
    x = int(bin, 2)
    if bin[0] == '1': # "sign bit", big-endian
       x -= 2**len(bin)
    return x

def to_int(bin): # from definition
    n = 0
    for i, b in enumerate(reversed(bin)):
        if b == '1':
           if i != (len(bin)-1):
              n += 2**i
           else: # MSB
              n -= 2**i 
    return n

Answer 3

>>> bits_in_word=12
>>> int('111111111111',2)-(1<<bits_in_word)
-1

This works because:

The two's complement of a binary number is defined as the value obtained by subtracting the number from a large power of two (specifically, from 2^N for an N-bit two's complement). The two's complement of the number then behaves like the negative of the original number in most arithmetic, and it can coexist with positive numbers in a natural way.

Answer 4

It's not built in, but if you want unusual length numbers then you could use the bitstring module.

>>> from bitstring import BitString
>>> a = BitString(bin='111111111111')
>>> a.int
-1

The same object can equivalently be created in several ways, including

>>> b = BitString(int=-1, length=12)

It just behaves like a string of bits of arbitrary length, and uses properties to get different interpretations:

>>> print a.int, a.uint, a.bin, a.hex, a.oct
-1 4095 0b111111111111 0xfff 0o7777