# All possible combination based on 2^n

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BeeTiaw on 14 May 2021
Edited: BeeTiaw on 14 May 2021
I want to create a matrix containing all possible combination. Example of this is shown below. The size of the matrix depends on the number of variable n and the total of combination should follow the . The example below is valid for and, hence, the total number of rows is 8. The value of each element is 0 and 1.
How to create this matrix automatically depending on the number of variable n?

Stephen23 on 14 May 2021
Edited: Stephen23 on 14 May 2021
n = 3;
m = dec2bin(0:pow2(n)-1)-'0' % limited precision
m = 8×3
0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
Or
C = cell(1,n);
[C{:}] = ndgrid(0:1);
C = cellfun(@(a)a(:),C,'uni',0);
M = [C{:}]
M = 8×3
0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1
BeeTiaw on 14 May 2021
It works!

Dyuman Joshi on 14 May 2021
y = flipud(dec2bin(0:2^n-1,n))-'0' %method 1
y = dec2bin(2^n-1:-1:0,n)-'0' %method 2
Choose any of the methods you wish, both give the same result.
P.S - There is a similar question in Cody as well.
##### 2 CommentsShowHide 1 older comment
BeeTiaw on 14 May 2021
Edited: BeeTiaw on 14 May 2021
I have another question. Quite similar but the output will be slightly different.

Stephan on 14 May 2021
n = 3
n = 3
ff2n(n)
ans = 8×3
0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
Stephen23 on 14 May 2021
Edited: Stephen23 on 14 May 2021
Note: requires the Statistics and Machine Learning Toolbox.

Bjorn Gustavsson on 14 May 2021
You could use dec2bin:
allpossibles = dec2bin(0:(2^n-1));
You'll have to extract the indices from the columns but that should be "not hard". There's more than likely many prettier solutions, for example have a look on the file exchange for nextperm (by Jos) and next-combination-permutation (by Matt-Fig).
HTH

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