For error correcting codes (Hamming), you make 1+1=0 as a starting point. Setting 1+1=2 creates patterns that often useful in real life (e.g. counting discrete

For error correcting codes (Hamming), you make 1+1=0 as a starting point. Setting 1+1=2 creates patterns that often useful in real life (e.g. counting discrete objects). But it's by no means some universal law. In this case setting 1+1=0 creates other patterns useful for error correcting codes.