Add Binary
<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>
Bit Manipulation; Math; String; Simulation
public class Solution {
    public string AddBinary(string a, string b) {
        int i = a.Length - 1;
        int j = b.Length - 1;
        var sb = new StringBuilder();
        for (int carry = 0; i >= 0 || j >= 0 || carry > 0; --i, --j) {
            carry += i >= 0 ? a[i] - '0' : 0;
            carry += j >= 0 ? b[j] - '0' : 0;
            sb.Append(carry % 2);
            carry /= 2;
        }
        var ans = sb.ToString().ToCharArray();
        Array.Reverse(ans);
        return new string(ans);
    }
}