Add Without Plus

17.1 Add Without Plus: Write a function that adds two numbers. You should not use + or any arithmetic operators.

• Implemented a full adder from scratch (min SOP through K-maps)

// initially I pushed back the bits into a vector
// this isnt the entire solution to the problem
// I've left the sum vector for learning purposes when I look back
// full adder
vector<int> sum(int a, int b) {
    int c_in = 0;
    vector<int> c_out;
    vector<int> sum;
    int s;
    int temp;

    int count = 0;
    c_out.push_back(c_in);

    int bit_a, bit_b;
    while (b != 0 || a != 0) {
        // look only at first bit
        bit_a = a & 1;
        bit_b = b & 1;

        // add bits using min SOP 
        /*
        sum.push_back((!bit_a && bit_b && !c_out.at(count)) ||
        (!bit_a && !bit_b && c_out.at(count)) ||
        (bit_a && !bit_b && !c_out.at(count)) ||
        (bit_a && bit_b && c_out.at(count)));
        */
        // equivalent
        sum.push_back(bit_a ^ bit_b ^ c_out.at(count));

        // find next c_out
        c_out.push_back((bit_b && c_out.at(count)) || (bit_a && bit_b) || (bit_a && c_out.at(count)));
        count++;

        // look at next bit
        a = a >> 1; b = b >> 1;
    }

    // add final carry
    sum.push_back(c_out.at(count));
    return sum;
}

// clean version
int add(int a, int b) {
    int c_in, c_out, s, final_s, base;
    c_in = c_out = final_s = base = 0;

    // s = current bit sum
    // final_s = current bit sum + previous sum

    int bit_a, bit_b;
    while (b != 0 || a != 0) {
        // look only at first bit
        bit_a = a & 1;
        bit_b = b & 1;

        // sum bits
        s = bit_a ^ bit_b ^ c_out;

        // find next c_out
        c_out = (bit_b && c_out) || (bit_a && bit_b) || (bit_a && c_out);

        // concatinate current bit to prev bit to form an actual number with significant base
        final_s = (s << base++) | final_s;

        // look at next bit
        a = a >> 1; b = b >> 1;
    }

    // add final carry
    final_s = (c_out << base++) | final_s;

    return final_s;
}

int main()
{
    //vector<int> s = sum(10, 10);
    //for (int i = s.size() - 1; i >= 0; i--) cout << s.at(i);
    //cout << endl;

    //s = sum(5, 10);
    //for (int i = s.size() - 1; i >= 0; i--) cout << s.at(i);
    //cout << endl;

    //s = sum(10, 7);
    //for (int i = s.size() - 1; i >= 0; i--) cout << s.at(i);
    //cout << endl;

    cout << add(10, 10) << endl;
    cout << add(7, 10) << endl;
    cout << add(20, 10) << endl;
    cout << add(45, 3) << endl;
}