def num_to_digit_rec(num, base): \"\"\" Return a list of digits for num with given base; Return an empty list [] if base < 2 or num <= 0 \"\"\" # Write your code here return []def digit_sum(num, base): \"\"\" Return the sum of all digits for a num with given base Your implementation should use num_to_digit_rec() function \"\"\" # Write your code here return 0 def digit_str(num, base): \"\"\" Given a number and a base, for base between [2, 36] inclusive Converts the number to its string representation using digits 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ to represent digits 0 to 35. Return the string representation of the number Return an empty string '' if base is not between [2, 36] Your implementation should use num_to_digit_rec() function \"\"\" digits = \"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ\" # Can not find str representations for base not in [2, 36] if base > 36 or base < 2: return \"\" # Calculate and return the str representation for num for the given base # Write your code here return \"\" def uses_only(word, letters): \"\"\" Return True if word only uses characters from letters; otherwise return False \"\"\" # Write your code here return Truedef digit_to_num(rep, base): \"\"\" Return -1 if base is not between [2,36] inclusive; or if the string rep contains characters not a digit for the base; Return the number represented by the string for the given base otherwise. For example digit_to_num(\"1001\", 2) is 9; digit_to_num(\"ABC\", 16) is 2748. \"\"\" # Check if the base is valid if base > 36 or base < 2: return -1 digits = \"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ\" rep = rep.upper() # Check if the rep only uses proper digits # Write your code here return 0 def run(): num = int(input(\"Enter a num: \")) base = int(input(\"Enter a base: \")) print(f\"Digit list is {num_to_digit_rec(num, base)}\") print(f\"Digit sum is {digit_sum(num, base)}\") print(f\"String Rep is {digit_str(num, base)}\") rep = input(f\"Enter a string rep of a num with base {base}: \") print(f\"The number is {digit_to_num(rep, base)}\")if __name__ == \"__main__\": run()- num_to_digit_rec(num, base): Given a num andits base, convert the num to a list of digits in its baserepresentation. 0 is converted to an empty list. You mustimplement this function using recursion. Do not use anyloops/iterations.
- digit_sum(num, base), Given a num and itsbase, find out sum of all of its digits in its base representation.You should use the num_to_digit_rec() function'sresult which is a list of all the digits. This function is an easyone-liner.
- digit_str(num, base): Given a num and itsbase, convert the num to a string representation for that base,using Capital Letters A-Z to represent digit 10-35. This functiononly works for base between [2, 36]. Do make sure that 0 isconverted to \"0\" for a valid base.
- uses_only(word, letters): The same function inChapter 9. It is a helper function needed to check a stringrepresentation's validity for the digit_to_num() function.
- digit_to_num(rep, base): Given a stringrepresentation rep and its base, convert the string representationwith a base to a number. For example digit_to_num(\"1001\", 2) = 9,digit_to_num(\"z\", 36) = 35. You may use uses_only() function tocheck that the string representation only uses valid digits for thegiven base.
Example:
Enter a num: 0Enter a base: 5Digit list is []Digit sum is 0String Rep is 0Enter a string rep of a num with base 5: 3The number is 3
