How do I create a matrix with all binary combinations?

Hi

I want to create a matrix with all binary combinations. If N is the length of the binary code, there would be possible combinations. Below are , and the 16 possible binary combinations are displayed.

  1  1  1  1  1  1  1  1  0  0  0  0  0  0  0  0 
 
  1  1  1  1  0  0  0  0  1  1  1  1  0  0  0  0 
 
  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0  0 
 
  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0 

How can I create such a matrix automatically? I don't really care which order they are in, as long as every combination is present, and N is a variable.

Thanks in advance.

Answer 1

[the cyclist]

There's an incredible obfuscated hack for this:

N = 4;
dec2bin(0:2^N-1)' - '0'

[Christian P]

Thanks to both of you, this worked like a charm! My N is usually less than 10, so memory shouldn't be a big problem :)

Answer 2

[Fangjun Jiang]

I though it should be

ff2n(4)

[Christian P]

This also worked, thanks :)

[Fangjun Jiang]

ff2n, Two-level full-factorial design, is built for this.

Answer 3

[James Tursa]

dec2bin(0:2^N-1) - '0'

Note that this is only practical for relatively small values of N. Even moderatly large N can cause this to exceed your available memory.

[Pranay Agarwal]

Hi, any similar method is there to extend this code for ternary strings, i.e., to generate all strings containing (0,1,2) of length N

[Torsten]

Is this a statement or a question ?

[the cyclist]

If you have the Statistics and Machine Learning Toolbox, you can use fullfact:

L = 3; % Length
N = 2; % Values in range 0-N
v = (N+1)*ones(1,L);
output = fullfact(v) - 1

output = 27×3

0 0 0 1 0 0 2 0 0 0 1 0 1 1 0 2 1 0 0 2 0 1 2 0 2 2 0 0 0 1

[Voss]

@Pranay Agarwal: You can use dec2base:

N = 4; % length
base = 3;
output = dec2base(0:base^N-1,base)-'0';

disp(output);

     0     0     0     0
     0     0     0     1
     0     0     0     2
     0     0     1     0
     0     0     1     1
     0     0     1     2
     0     0     2     0
     0     0     2     1
     0     0     2     2
     0     1     0     0
     0     1     0     1
     0     1     0     2
     0     1     1     0
     0     1     1     1
     0     1     1     2
     0     1     2     0
     0     1     2     1
     0     1     2     2
     0     2     0     0
     0     2     0     1
     0     2     0     2
     0     2     1     0
     0     2     1     1
     0     2     1     2
     0     2     2     0
     0     2     2     1
     0     2     2     2
     1     0     0     0
     1     0     0     1
     1     0     0     2
     1     0     1     0
     1     0     1     1
     1     0     1     2
     1     0     2     0
     1     0     2     1
     1     0     2     2
     1     1     0     0
     1     1     0     1
     1     1     0     2
     1     1     1     0
     1     1     1     1
     1     1     1     2
     1     1     2     0
     1     1     2     1
     1     1     2     2
     1     2     0     0
     1     2     0     1
     1     2     0     2
     1     2     1     0
     1     2     1     1
     1     2     1     2
     1     2     2     0
     1     2     2     1
     1     2     2     2
     2     0     0     0
     2     0     0     1
     2     0     0     2
     2     0     1     0
     2     0     1     1
     2     0     1     2
     2     0     2     0
     2     0     2     1
     2     0     2     2
     2     1     0     0
     2     1     0     1
     2     1     0     2
     2     1     1     0
     2     1     1     1
     2     1     1     2
     2     1     2     0
     2     1     2     1
     2     1     2     2
     2     2     0     0
     2     2     0     1
     2     2     0     2
     2     2     1     0
     2     2     1     1
     2     2     1     2
     2     2     2     0
     2     2     2     1
     2     2     2     2

[Pranay Agarwal]

Thanks a lot....