what is the result of arithmetic coding for image compression and encryption? and how can we find out the size of the output matrix?

Hi everybody

I want to know the what is the results of applying arithmetic coding on image? is it a binary or decimal string? or a binary matrix or?

althuogh I want to know what is the new size for input image matrix that compression made?

Also, I have a code that XOR two out put from 2 step, and one step is the result of arithmetic coding, step 2 is from a fuzzy system and it could xor them with no error. how does it happen? I mean it doesn't need to be the same size? why I don't get any error I expect to be so.

thank you in advance