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How do I create a matrix with all binary combinations?

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Christian P on 13 May 2020

Commented: Fangjun Jiang on 14 May 2020

Accepted Answer: 骑自行车的人

I want to create a matrix with all binary combinations. If N is the length of the binary code, there would be

可能的组合。下面是

, 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.

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骑自行车的人 on 13 May 2020

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There's an incredible obfuscated hack for this:

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

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Christian P on 13 May 2020

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 :)

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Fangjun Jiang on 13 May 2020

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I though it should be

ff2n(4)

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Fangjun Jiang on 14 May 2020

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

James Tursa on 13 May 2020

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Edited:James Tursa on 13 May 2020

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.