How to perform XOR in a recursive scenario

I have a 1x5 char matrix. I need to perform a bitwise XOR operation on all the elements in the matrix.If T is the char matrix , I need a matrix T' such that

         T'= T XOR (T-1)'  for all T
             T             for T=1

Let the char matrix be T

   T=['0000000000110111' '0000000001000001' '0000000001001010'  '0000000010111000'  '0000000000101111']
   T'=['0000000000110111' '0000000001110110' '0000000000111100' '0000000010000100' '0000000010101011']

ie; Leaving the first element as such , I need to XOR all the other elements with the newly formed matrix. I tried the following code but I'm unable to get the correct result.

     Yxor1d = [T(1) cellfun(@(a,b) char((a ~= b) + '0'), T(2:end), T'(1:end-1), 'UniformOutput', false)]

I need to perform the XOR operation such that , for obtaining the elements of T'

T' (2)= T(2) XOR T' (1)
T' (3)= T(3) XOR T' (2)

It'll be really helpful to know where I went wrong.Thanks.

Solution

You are using cellfun when a cell array is expected as the input. You are using a character array, and what you're actually doing is taking each of those 5 strings and creating a single character array out of them. Chaining those strings together is actually performing a character concatenation.

You probably don't want that. To fix this, all you have to do is make T a cell array by placing {} characters instead of array ([]) characters to declare your characters:

T={'0000000000110111' '0000000001000001' '0000000001001010'  '0000000010111000'  '0000000000101111'};

Because you have edited your post after I provided my answer, my previous answer using cellfun is now incorrect. Because you are using a recurrence relation where you are referring to the previous output rather than input, you can no longer use cellfun. You'll need to use a for loop. There are probably more elegant ways to do it, but this is the easiest if you want to get something working.

As such, initialize an output cell array that is the same size as the input cell array like above, then you'll need to initialize the first cell to be the first cell of the input, then iterate through each pair of input and output elements yourself.

So do something like this:

Yxor1d = cell(1,numel(T));
Yxor1d{1} = T{1};
for idx = 2 : numel(T)
    Yxor1d{idx} = char(double(T{idx} ~= Yxor1d{idx-1}) + '0');
end

For each value i of T', we XOR with the current input at T{i} with the previous output of T'{i-1}.

Use the above and your input cell array T, we get:

Yxor1d = 

  Columns 1 through 3

    '0000000000110111'    '0000000001110110'    '0000000000111100'

  Columns 4 through 5

    '0000000010000100'    '0000000010101011'

This matches with your specifications in your modified post.