<p>Given two binary strings <code>a</code> and <code>b</code>, return <em>their sum as a binary string</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> a = "11", b = "1"
<strong>Output:</strong> "100"
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> a = "1010", b = "1011"
<strong>Output:</strong> "10101"
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= a.length, b.length &lt;= 10<sup>4</sup></code></li>
	<li><code>a</code> and <code>b</code> consist&nbsp;only of <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code> characters.</li>
	<li>Each string does not contain leading zeros except for the zero itself.</li>
</ul>

class Solution {
public:
    string addBinary(string a, string b) {
        // good question
        // calculate the corresponding decimal value of each bit using powers of 2.
        int n=a.length();
        int m=b.length();
        int i=n-1;
        int j=m-1;
        int carry=0;
        string res="";
        while(i>=0 || j>=0 || carry)
        {
            int sum=carry;
            if(i>=0)
            {
                sum+=a[i]-'0';
                i--;
            }
            if(j>=0)
            {
                sum+=b[j]-'0';
                j--;
            }
            carry=sum/2;
            res=to_string(sum%2)+res;
        }
        return res;
    }
};
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