enumBase2

Constructs a character or numeric array that enumerates from 0 to (2^n - 1) in binary.

Description

a = enumBase2(n) constructs a cell array that enumerates from 0 to (2^n - 1) in binary.

 a = enumBase2(n,outputformat) constructs an array that enumerates from 0
 to (2^n - 1) in binary. The type of array output is given by
 outputformat. By default, outputformat=1, which outputs a cell array.
 If outputformat=2, then the output is a numeric array.
 
   Examples
   -------
   numBase2(4) returns the following cell array:
 0000
 0001
 0010
 0011
 0100
 0101
 0110
 0111
 1000
 1001
 1010
 1011
 1100
 1101
 1110
 1111

   numBase2(4,2) output the same as above, except as a numeric array.
 
 Useful for combinatorics.

• MATLAB release: MATLAB 7.2 (R2006a)

[John D'Errico]

A minor point, but this should be just a wrapper for the one line idiom:

dec2bin(0:(2^n-1))

Except that this code uses a loop, and fails to preallocate its array, so it will be REALLY, REALLY slow for even moderately large n. Note the examples below as n grows from 5 to 15.

>> n=5;
>> tic,c = dec2bin(0:(2^n-1));toc
Elapsed time is 0.000500 seconds.
>> tic,c=enumBase2(n);toc
Elapsed time is 0.002035 seconds.

>> n=10;
>> tic,c = dec2bin(0:(2^n-1));toc
Elapsed time is 0.005724 seconds.
>> tic,c=enumBase2(n);toc
Elapsed time is 0.131692 seconds.

>> n=15;
>> tic,c = dec2bin(0:(2^n-1));toc,tic,c=enumBase2(n);toc
Elapsed time is 0.269849 seconds.
>> tic,c=enumBase2(n);toc
Elapsed time is 123.935903 seconds.

If you want a code that does more than the dec2bin idiom, but is actually efficient, take a look at allcomb [FEX:10054].

[Shawn Mikula]

thanks John! I have incorporated your suggestion to enhance performance and have added the option to output either a numeric array or a cell array.

[Shawn Mikula]

Didn't realize my comment would be posted immediately. Should have said that the updated enumBase2 should appear in 1-2 days. But for those who don't want to wait, here it is:

function [a] = enumBase2(varargin)

% a = enumBase2(n) constructs a cell array that enumerates from 0 to (2^n - 1) in binary.
%
% a = enumBase2(n,outputformat) constructs an array that enumerates from 0
% to (2^n - 1) in binary. The type of array output is given by
% outputformat. By default, outputformat=1, which outputs a cell array.
% If outputformat=2, then the output is a numeric array.
%
% Examples
% -------
% numBase2(4) returns the following cell array:
% 0000
% 0001
% 0010
% 0011
% 0100
% 0101
% 0110
% 0111
% 1000
% 1001
% 1010
% 1011
% 1100
% 1101
% 1110
% 1111
%
% numBase2(4,2) output the same as above, except as a numeric array.
%
% Useful for combinatorics.

try
    n = varargin{1}
catch
error('try "help enumBase2"')
end
try
    formout = varargin{2}
catch
formout = 1;
end
if formout==1
a=dec2bin(0:(2^n-1));
elseif formout==2
    aTemp=dec2bin(0:(2^n-1));
    a=ones(2^n-1,n);
    for i=1:n
        for j=1:2^n
            a(j,i)=str2num(aTemp(j,i));
        end
    end
else
    error('try "help enumBase2"')
    
end

[Duane Hanselman]

Please don't use user reviews as a way to distribute code. User reviews cannot be deleted, modified or updated. Your code belongs under the Download Now button, not here!

[John Lei]

just what I was looking for