def octal_to_hex(octal: str) -> str:
    """
    Convert an Octal number to Hexadecimal number.
    For more information: https://en.wikipedia.org/wiki/Octal

    >>> octal_to_hex("100")
    '0x40'
    >>> octal_to_hex("235")
    '0x9D'
    >>> octal_to_hex(17)
    Traceback (most recent call last):
        ...
    TypeError: Expected a string as input
    >>> octal_to_hex("Av")
    Traceback (most recent call last):
        ...
    ValueError: Not a Valid Octal Number
    >>> octal_to_hex("")
    Traceback (most recent call last):
        ...
    ValueError: Empty string was passed to the function
    """

    if not isinstance(octal, str):
        raise TypeError("Expected a string as input")
    if octal.startswith("0o"):
        octal = octal[2:]
    if octal == "":
        raise ValueError("Empty string was passed to the function")
    if any(char not in "01234567" for char in octal):
        raise ValueError("Not a Valid Octal Number")

    decimal = 0
    for char in octal:
        decimal <<= 3
        decimal |= int(char)

    hex_char = "0123456789ABCDEF"

    revhex = ""
    while decimal:
        revhex += hex_char[decimal & 15]
        decimal >>= 4

    return "0x" + revhex[::-1]


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    nums = ["030", "100", "247", "235", "007"]

    ## Main Tests

    for num in nums:
        hexadecimal = octal_to_hex(num)
        expected = "0x" + hex(int(num, 8))[2:].upper()

        assert hexadecimal == expected

        print(f"Hex of '0o{num}' is: {hexadecimal}")
        print(f"Expected was: {expected}")
        print("---")