feat: Add Binary addition algorithm in Python

This program adds two binary numbers given as strings and returns their sum as a binary string.
Based on LeetCode Problem 67 — Add Binary.

Author: Sujalgupta2p

bit_manipulation/add_Binary.py

@@ -0,0 +1,27 @@
+def add_Binary(a: str, b: str) -> str:
+    i, j = len(a) - 1, len(b) - 1  # start from the end of both strings
+    carry = 0
+    result = []
+
+    while i >= 0 or j >= 0 or carry:
+        total = carry
+
+        if i >= 0:
+            total += int(a[i])  # convert char to int
+            i -= 1
+        if j >= 0:
+            total += int(b[j])
+            j -= 1
+
+        result.append(str(total % 2))  # current bit
+        carry = total // 2             # update carry
+
+    return ''.join(reversed(result))   # reverse the result to get correct order
+
+
+# Example usage
+if __name__ == "__main__":
+    a = "1010"
+    b = "1011"
+    print("Input: a =", a, ", b =", b)
+    print("Output:", add_Binary(a, b))