diff --git a/bit_manipulation/count_number_of_one_bits.py b/bit_manipulation/count_number_of_one_bits.py
index f0c9f927620a..b34ff7e1c5d2 100644
--- a/bit_manipulation/count_number_of_one_bits.py
+++ b/bit_manipulation/count_number_of_one_bits.py
@@ -20,6 +20,8 @@ def get_set_bits_count_using_brian_kernighans_algorithm(number: int) -> int:
     Traceback (most recent call last):
         ...
     ValueError: the value of input must not be negative
+    >>> get_set_bits_count_using_brian_kernighans_algorithm(1023)
+    10
     """
     if number < 0:
         raise ValueError("the value of input must not be negative")
@@ -49,6 +51,8 @@ def get_set_bits_count_using_modulo_operator(number: int) -> int:
     Traceback (most recent call last):
         ...
     ValueError: the value of input must not be negative
+    >>> get_set_bits_count_using_modulo_operator(1024)
+    1
     """
     if number < 0:
         raise ValueError("the value of input must not be negative")
diff --git a/bit_manipulation/is_power_of_two.py b/bit_manipulation/is_power_of_two.py
index 023e979fe51c..3dd8df3540bc 100644
--- a/bit_manipulation/is_power_of_two.py
+++ b/bit_manipulation/is_power_of_two.py
@@ -33,6 +33,10 @@ def is_power_of_two(number: int) -> bool:
     True
     >>> is_power_of_two(17)
     False
+    >>> is_power_of_two(1024)
+    True
+    >>> is_power_of_two(1023)
+    False
     >>> is_power_of_two(-1)
     Traceback (most recent call last):
         ...
diff --git a/bit_manipulation/next_power_of_two.py b/bit_manipulation/next_power_of_two.py
new file mode 100644
index 000000000000..4b523c17b130
--- /dev/null
+++ b/bit_manipulation/next_power_of_two.py
@@ -0,0 +1,55 @@
+"""
+Author  : Basuki Nath
+Date    : 2025-10-04
+
+Utility to compute the next power of two greater than or equal to n.
+"""
+
+
+def next_power_of_two(n: int) -> int:
+    """
+    Return the smallest power of two >= n for positive integers.
+
+    >>> next_power_of_two(1)
+    1
+    >>> next_power_of_two(2)
+    2
+    >>> next_power_of_two(3)
+    4
+    >>> next_power_of_two(5)
+    8
+    >>> next_power_of_two(1025)
+    2048
+    >>> next_power_of_two(0)
+    Traceback (most recent call last):
+        ...
+    ValueError: n must be positive
+    >>> next_power_of_two(-3)
+    Traceback (most recent call last):
+        ...
+    ValueError: n must be positive
+    """
+    if n <= 0:
+        raise ValueError("n must be positive")
+    # If already a power of two, return it
+    if n & (n - 1) == 0:
+        return n
+    # Otherwise, fill bits to the right
+    v = n - 1
+    v |= v >> 1
+    v |= v >> 2
+    v |= v >> 4
+    v |= v >> 8
+    v |= v >> 16
+    # for very large ints, continue shifting using Python's arbitrary precision
+    shift = 32
+    while (1 << shift) <= v:
+        v |= v >> shift
+        shift <<= 1
+    return v + 1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
diff --git a/bit_manipulation/parity.py b/bit_manipulation/parity.py
new file mode 100644
index 000000000000..019c88deea30
--- /dev/null
+++ b/bit_manipulation/parity.py
@@ -0,0 +1,43 @@
+"""
+Author  : Basuki Nath
+Date    : 2025-10-04
+
+Simple parity utility for integers.
+
+The parity is 1 when the number of set bits is odd, otherwise 0.
+"""
+
+
+def parity(number: int) -> int:
+    """
+    Return 1 if `number` has an odd number of set bits, otherwise 0.
+
+    >>> parity(0)
+    0
+    >>> parity(1)
+    1
+    >>> parity(2)  # 10b -> one set bit
+    1
+    >>> parity(3)  # 11b -> two set bits
+    0
+    >>> parity(1023)  # 10 ones -> even
+    0
+    >>> parity(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: number must not be negative
+    """
+    if number < 0:
+        raise ValueError("number must not be negative")
+    # Kernighan's algorithm toggling parity
+    p = 0
+    while number:
+        p ^= 1
+        number &= number - 1
+    return p
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
diff --git a/bit_manipulation/rotate_bits.py b/bit_manipulation/rotate_bits.py
new file mode 100644
index 000000000000..521ab8de203f
--- /dev/null
+++ b/bit_manipulation/rotate_bits.py
@@ -0,0 +1,70 @@
+"""
+Author  : Basuki Nath
+Date    : 2025-10-04
+
+Bit rotation helpers for 32-bit unsigned integers.
+"""
+
+
+def rotate_left32(x: int, k: int) -> int:
+    """
+    Rotate the lower 32 bits of x left by k and return result in 0..2**32-1.
+
+    >>> rotate_left32(1, 1)
+    2
+    >>> rotate_left32(1, 31)
+    2147483648
+    >>> rotate_left32(0x80000000, 1)
+    1
+    >>> rotate_left32(0x12345678, 4)
+    591751041
+    >>> rotate_left32(-1, 3)
+    Traceback (most recent call last):
+        ...
+    ValueError: x must be a non-negative integer
+    >>> rotate_left32(1, -1)
+    Traceback (most recent call last):
+        ...
+    ValueError: k must be non-negative
+    """
+    if not isinstance(x, int) or x < 0:
+        raise ValueError("x must be a non-negative integer")
+    if not isinstance(k, int) or k < 0:
+        raise ValueError("k must be non-negative")
+    mask = (1 << 32) - 1
+    k &= 31
+    return ((x << k) & mask) | ((x & mask) >> (32 - k))
+
+
+def rotate_right32(x: int, k: int) -> int:
+    """
+    Rotate the lower 32 bits of x right by k and return result in 0..2**32-1.
+
+    >>> rotate_right32(2, 1)
+    1
+    >>> rotate_right32(1, 1)
+    2147483648
+    >>> rotate_right32(0x12345678, 4)
+    2166572391
+    >>> rotate_right32(-1, 1)
+    Traceback (most recent call last):
+        ...
+    ValueError: x must be a non-negative integer
+    >>> rotate_right32(1, -3)
+    Traceback (most recent call last):
+        ...
+    ValueError: k must be non-negative
+    """
+    if not isinstance(x, int) or x < 0:
+        raise ValueError("x must be a non-negative integer")
+    if not isinstance(k, int) or k < 0:
+        raise ValueError("k must be non-negative")
+    mask = (1 << 32) - 1
+    k &= 31
+    return ((x & mask) >> k) | ((x << (32 - k)) & mask)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()