Add binary parity pattern implementation and update directory

Author: surlogu

DIRECTORY.md

@@ -37,6 +37,7 @@
   * [Binary Twos Complement](bit_manipulation/binary_twos_complement.py)
   * [Binary Xor Operator](bit_manipulation/binary_xor_operator.py)
   * [Bitwise Addition Recursive](bit_manipulation/bitwise_addition_recursive.py)
+  * [Binary Parity Pattern](bit_manipulation/binary_parity_pattern.py)
   * [Count 1S Brian Kernighan Method](bit_manipulation/count_1s_brian_kernighan_method.py)
   * [Count Number Of One Bits](bit_manipulation/count_number_of_one_bits.py)
   * [Excess 3 Code](bit_manipulation/excess_3_code.py)

bit_manipulation/binary_parity_pattern.py

@@ -0,0 +1,42 @@
+"""
+=======================================
+⚖️ Binary Parity Pattern
+=======================================
+
+Generates a binary pattern where each bit represents 
+the parity (even/odd) of the cumulative sum of bits 
+in the original binary representation.
+
+Example:
+    13 (1101) → cumulative sums [1,2,3,4]
+    parity pattern = 1010
+"""
+
+def binary_parity_pattern(number: int) -> str:
+    """
+    Generate parity pattern of cumulative binary sums.
+
+    >>> binary_parity_pattern(13)
+    '0b1010'
+    >>> binary_parity_pattern(7)
+    '0b111'
+    >>> binary_parity_pattern(4)
+    '0b10'
+    """
+    if number < 0:
+        number = abs(number)
+
+    binary = bin(number)[2:]
+    parity_pattern = ""
+    cum_sum = 0
+
+    for bit in binary:
+        cum_sum += int(bit)
+        parity_pattern += str(cum_sum % 2)
+
+    return "0b" + parity_pattern
+
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()