Bits list to integer in Python

Question

I have such list in Python: [1,0,0,0,0,0,0,0]. Can I convert it to integer like as I've typed 0b10000000 (i.e. convert to 128)? I need also to convert sequences like [1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0] to integers (here it will return 0b1100000010000000, i.e. 259). Length of list is always a multiple of 8, if it is necessary.

Answer 1

You can use bitshifting:

out = 0
for bit in bitlist:
    out = (out << 1) | bit

This easily beats the "int cast" method proposed by A. R. S., or the modified cast with lookup proposed by Steven Rumbalski:

>>> def intcaststr(bitlist):
...     return int("".join(str(i) for i in bitlist), 2)
... 
>>> def intcastlookup(bitlist):
...     return int(''.join('01'[i] for i in bitlist), 2)
... 
>>> def shifting(bitlist):
...     out = 0
...     for bit in bitlist:
...         out = (out << 1) | bit
...     return out
... 
>>> timeit.timeit('convert([1,0,0,0,0,0,0,0])', 'from __main__ import intcaststr as convert', number=100000)
0.5659139156341553
>>> timeit.timeit('convert([1,0,0,0,0,0,0,0])', 'from __main__ import intcastlookup as convert', number=100000)
0.4642159938812256
>>> timeit.timeit('convert([1,0,0,0,0,0,0,0])', 'from __main__ import shifting as convert', number=100000)
0.1406559944152832

Answer 2

...or using the bitstring module

>>> from bitstring import BitArray
>>> bitlist=[1,0,0,0,0,0,0,0]
>>> b = BitArray(bitlist)
>>> b.uint
128

Answer 3

I came across a method that slightly outperforms Martijn Pieters solution, though his solution is prettier of course. I am actually a bit surprised by the results, but anyway...

import timeit

bit_list = [1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0]

def mult_and_add(bit_list):
    output = 0
    for bit in bit_list:
        output = output * 2 + bit
    return output

def shifting(bitlist):
     out = 0
     for bit in bitlist:
         out = (out << 1) | bit
     return out

n = 1000000

t1 = timeit.timeit('convert(bit_list)', 'from __main__ import mult_and_add as convert, bit_list', number=n)
print "mult and add method time is : {} ".format(t1)
t2 = timeit.timeit('convert(bit_list)', 'from __main__ import shifting as convert, bit_list', number=n)
print "shifting method time is : {} ".format(t2)

Result:

mult and add method time is : 1.69138722958 
shifting method time is : 1.94066818592 

Answer 4

Try this one-liner:

int("".join(str(i) for i in my_list), 2)

If you're concerned with speed/efficiency, take a look at Martijn Pieters' solution.

Answer 5

how about this:

out = sum([b<<i for i, b in enumerate(my_list)])

or in reverse order:

out = sum([b<<i for i, b in enumerate(my_list[::-1])])

Answer 6

Fastest one-liner:

def reduced_plus(bitlist):
    return functools.reduce(lambda acc, val: acc * 2 + val, bitlist)

Benchmarking:

import timeit
import functools

def shifting_plus(bitlist):
    out = 0
    for bit in bitlist:
        out = out * 2 + bit
    return out

def shifting(bitlist):
    out = 0
    for bit in bitlist:
        out = (out << 1) | bit
    return out

def reduced_plus(bitlist):
    return functools.reduce(lambda acc, val: acc * 2 + val, bitlist)

def reduced(bitlist):
    return functools.reduce(lambda acc, val: acc << 1 | val, bitlist)

def summed(bitlist):
    return sum([b<<i for i, b in enumerate(bitlist)])

def intcastlookup(bitlist):
    return int(''.join('01'[i] for i in bitlist), 2)

cycles = 1_000_000
for fname in ["shifting_plus", "shifting", "reduced_plus", "reduced", "summed", "intcastlookup"]:
    result = timeit.timeit('convert([1,0,0,0,0,0,0,0])', f'from __main__ import {fname} as convert')
    print(f"{result:.3f} s - {fname}")

results:

0.465 s - shifting_plus
0.779 s - shifting
0.807 s - reduced_plus
0.841 s - summed
0.884 s - intcastlookup
1.024 s - reduced

Answer 7

The simplest method suggested by @Akavall is the fastest one. The additional timing below for mult_add_xor shows that the bit operations are slower in python since simple addition "+ bit" is faster than xor "| bit" and the multiplication by 2 is faster than the bit shift "<< 1".

import timeit

bit_list = [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]


def mult_and_add(bit_list):
    output = 0
    for bit in bit_list:
        output = output * 2 + bit
    return output


def mult_and_xor(bit_list):
    output = 0
    for bit in bit_list:
        output = output * 2 | bit
    return output


def shifting(bitlist):
    out = 0
    for bit in bitlist:
        out = (out << 1) | bit
    return out


n = 1000000

a1 = mult_and_add(bit_list)
a2 = mult_and_xor(bit_list)
a3 = shifting(bit_list)

print('a1: ', a1, ' a2: ', a2, ' a3: ', a3)
assert a1 == a2 == a3

t = timeit.timeit('convert(bit_list)',
                  'from __main__ import mult_and_add as convert, bit_list',
                  number=n)
print("mult and add method time is : {} ".format(t))
t = timeit.timeit('convert(bit_list)',
                  'from __main__ import mult_and_xor as convert, bit_list',
                  number=n)
print("mult and xor method time is : {} ".format(t))
t = timeit.timeit('convert(bit_list)',
                  'from __main__ import shifting as convert, bit_list',
                  number=n)
print("shifting method time is : {} ".format(t))

Output:

a1:  49280  a2:  49280  a3:  49280
mult and add method time is : 0.9469406669959426 
mult and xor method time is : 1.0905388034880161 
shifting method time is : 1.2844801126047969