def unique_digits(str_num):
    """
    Test that the digits of the input number are unique and are not 0.
    Args:
        str_num: <str> integer to test

    Returns: False if the digits of the input number are not unique else True
    """
    str_num_set = set(str_num)
    if '0' in str_num_set:
        return False
    if len(str_num_set) != len(str_num):
        return False
    return True