Matrix with binomial permutation

I really had trouble finding the right words for the question. I'll try my best. Given a numerical number k (k>1), I want to get a [2^k, k] matrix with all possible binomial permutation. for K = 2, I hope to get: [1 1; 1 2; 2 1; 2 2]. for k = 3, the matrix will look like: [1 1 1; 1 1 2; 1 2 1; 1 2 2; 2 1 1; 2 1 2; 2 2 1; 2 2 2]. I could do for loop for each condition, like for k=3:

mat = [];
for digit1 = 1:2
  for digit2 = 1:2
      for digit3 = 1:2
          mat(size(mat,1)+1,:) = [digit1 digit2 digit3];
      end
  end
end

But this is not generalized and efficient. Is there any thoughts on generating such matrix? Thanks!

Answer 1

[Honglei Chen]

dec2bin(0:2^K-1)-'0'+1

HTH

[Zheng Liu]

That's why we like binary. Thanks!