Add binary to gray code conversion algorithm (#13826)

* Create Binary_to_gray.py

* Update and rename Binary_to_gray.py to binary_to_gray.py

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Author: Craniace

conversions/binary_to_gray.py

@@ -0,0 +1,50 @@
+"""
+Binary to Gray code conversion algorithm.
+
+Reference:
+https://en.wikipedia.org/wiki/Gray_code
+"""
+
+
+def binary_to_gray(binary: str) -> str:
+    """
+    Convert a binary number (as string) to its equivalent Gray code.
+
+    The Gray code is generated by XOR-ing each bit with the bit just before it.
+
+    Args:
+        binary (str): A string representing a binary number (e.g., "10101010").
+
+    Returns:
+        str: The corresponding Gray code string.
+
+    Example:
+        >>> binary_to_gray("10101010")
+        '11111111'
+
+        >>> binary_to_gray("1101")
+        '1011'
+    """
+    # Convert binary string to integer
+    binary_int = int(binary, 2)
+
+    # XOR the binary number with itself shifted right by 1 bit
+    gray_int = binary_int ^ (binary_int >> 1)
+
+    # Convert the integer result back to a binary string (remove '0b' prefix)
+    gray_code = bin(gray_int)[2:]
+
+    # Pad with leading zeros to maintain same bit length as input
+    return gray_code.zfill(len(binary))
+
+
+if __name__ == "__main__":
+    # Take input from user
+    binary_input = input("Enter a binary number: ").strip()
+
+    # Validate the input (only 0s and 1s allowed)
+    if not all(bit in "01" for bit in binary_input):
+        print("❌ Invalid input! Please enter only 0s and 1s.")
+    else:
+        result = binary_to_gray(binary_input)
+        print(f"✅ The Gray code for binary {binary_input} is: {result}")