feat: Add Binary addition algorithm in C++

this program adds two binary numbers given as strings and returns their sum as a binary string.

Author: Sujalgupta2p

bit_manipulation/add_binary.cpp

@@ -0,0 +1,28 @@
+#include <iostream>
+#include <string>
+#include <algorithm>
+
+std::string add_binary(std::string a, std::string b) {
+    int i = a.size() - 1;
+    int j = b.size() - 1;
+    int carry = 0;
+    std::string result = "";
+
+    while (i >= 0 || j >= 0 || carry) {
+        int sum = carry;
+        if (i >= 0) sum += a[i--] - '0'; // convert char to int
+        if (j >= 0) sum += b[j--] - '0';
+        result += (sum % 2) + '0'; // convert int back to char
+        carry = sum / 2;
+    }
+
+    std::reverse(result.begin(), result.end());
+    return result;
+}
+
+int main() {
+    std::string a = "1010";
+    std::string b = "1011";
+    std::cout << "Sum: " << add_binary(a, b) << std::endl; // Output: 10101
+    return 0;
+}