string addBinary(string a, string b) {

int carry = 0;

// always assume a is longer

if (a.size() < b. size())

swap(a, b);

string result;

int p = a.size() - 1, q = b.size() - 1;

for (; q >= 0; p--, q--) {

int ap = a[p] - '0';

int bq = b[q] - '0';

int sum = ap ^ bq ^ carry;

result.push_back(sum + '0');

carry = (ap & bq) | (carry & (ap ^ bq));

}

while (p >= 0) {

int ap = a[p] - '0';

int sum = ap ^ carry;

result.push_back(sum + '0');

carry = ap & carry;

--p;

}

if (carry)

result.push_back('1');

std::reverse(result.begin(), result.end());

return result;

}

Solution sol;

vector<string> a = {

"111111",

"0",

"1",

"1",

"101",

};

vector<string> b = {

"11",

"0",

"0",

"1",

"1"

};

for (int i = 0; i < a.size(); ++i) {

cout << sol.addBinary(a[i], b[i]) << '\n';

}

return 0;

}