# 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)

```cpp
// 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;
}
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://maksimdan.gitbook.io/interview-practice-problems/coding_practice_questions/hard/add-without-plus.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.