How can I generate all the possible binary lists with 4 elements? (Using Python)

Question

I'm wondering is there a way I can generate a list whose sublists are all the possible combinations of 0 and 1 with 4 elements? To generate an individual sublist, I have

import random
binum = np.random.randint(2, size=4).tolist()

But how can I get a full list to contain all the possible sublists, each appears once? So the desired output looks like:

[[0,0,0,0],[0,0,0,1]...[1,0,0,1]...[1,1,1,1]]

(There're 16 elements in total for this case). Thanks:)

Answer 1

Just iterate over numbers from 0 to 15 and get their binary representation:

In [1]: N = 4    

In [2]: def getbit(value, bitnum):
   ...:     mask = 1 << bitnum
   ...:     return (value & mask) >> bitnum
   ...: 

In [3]: [[getbit(i, j) for j in range(N)] for i in range(2 ** N)]
Out[3]: 
[[0, 0, 0, 0],
 [1, 0, 0, 0],
 [0, 1, 0, 0],
 [1, 1, 0, 0],
 [0, 0, 1, 0],
 [1, 0, 1, 0],
 [0, 1, 1, 0],
 [1, 1, 1, 0],
 [0, 0, 0, 1],
 [1, 0, 0, 1],
 [0, 1, 0, 1],
 [1, 1, 0, 1],
 [0, 0, 1, 1],
 [1, 0, 1, 1],
 [0, 1, 1, 1],
 [1, 1, 1, 1]]

Same in numpy:

np.unpackbits(np.expand_dims(np.arange(2 ** N, dtype=np.uint8), -1),
              axis=1, bitorder='little', count=N)

Also, you can generate the next element by implementing increment operation on binary array:

def gen(l=4):
    a = [0 for _ in range(l)]
    while True:
        yield a.copy()
        i = 0
        while i < l and a[i]:
            a[i] = 0
            i += 1
        if i == l:
            break
        a[i] = 1