diff --git a/DIRECTORY.md b/DIRECTORY.md
index 7d3ceee144be..16ff73467c54 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -548,7 +548,7 @@
   * [Basic Maths](maths/basic_maths.py)
   * [Binary Exp Mod](maths/binary_exp_mod.py)
   * [Binary Exponentiation](maths/binary_exponentiation.py)
-  * [Binary Exponentiation 2](maths/binary_exponentiation_2.py)
+  * [Binary Exponentiation 2](maths/binary_multiplication.py)
   * [Binary Exponentiation 3](maths/binary_exponentiation_3.py)
   * [Binomial Coefficient](maths/binomial_coefficient.py)
   * [Binomial Distribution](maths/binomial_distribution.py)
diff --git a/maths/binary_exponentiation_2.py b/maths/binary_multiplication.py
similarity index 71%
rename from maths/binary_exponentiation_2.py
rename to maths/binary_multiplication.py
index af8f776dd266..dcac6e383fe0 100644
--- a/maths/binary_exponentiation_2.py
+++ b/maths/binary_multiplication.py
@@ -12,6 +12,29 @@
 
 
 def b_expo(a: int, b: int) -> int:
+    """
+    Calculate the result of multiplying 'a' and 'b' using bitwise multiplication.
+    Parameters:
+    a (int): The first number.
+    b (int): The second number.
+    Returns:
+    int: The result of 'a' multiplied by 'b'.
+    Examples:
+    >>> b_expo(2, 3)
+    6
+    >>> b_expo(5, 0)
+    0
+    >>> b_expo(3, 4)
+    12
+    >>> b_expo(10, 5)
+    50
+    >>> b_expo(0, 5)
+    0
+    >>> b_expo(2, 1)
+    2
+    >>> b_expo(1, 10)
+    10
+    """
     res = 0
     while b > 0:
         if b & 1:
@@ -23,6 +46,12 @@ def b_expo(a: int, b: int) -> int:
     return res
 
 
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+
 def b_expo_mod(a: int, b: int, c: int) -> int:
     res = 0
     while b > 0: