Your numbers are in BINARY form, and you want to add modulo 2^16.
The simplest solution is to convert to a decimal integer. I'll assume they are stored as chars. But if they are boolean vectors, just as easy.
AplusB = mod(bin2dec(A) + bin2dec(B),2^16)
You can do it all in one line. Or, you could even write a little function.
binplus16 = @(a,b) dec2bin(mod(bin2dec(A) + bin2dec(B),2^16));
As you can see, the result is the same. We could have done it in a variety of ways. But this is simplest.