Question

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 True

def 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 and its base, convert the num to a list of digits in its base representation. 0 is converted to an empty list. You must implement this function using recursion. Do not use any loops/iterations.
• digit_sum(num, base), Given a num and its base, find out sum of all of its digits in its base representation. You should use the num_to_digit_rec() function's result which is a list of all the digits. This function is an easy one-liner.
• digit_str(num, base): Given a num and its base, convert the num to a string representation for that base, using Capital Letters A-Z to represent digit 10-35. This function only works for base between [2, 36]. Do make sure that 0 is converted to "0" for a valid base.
• uses_only(word, letters): The same function in Chapter 9. It is a helper function needed to check a string representation's validity for the digit_to_num() function.
• digit_to_num(rep, base): Given a string representation rep and its base, convert the string representation with 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 to check that the string representation only uses valid digits for the given base.

Example:

Enter a num: 0
Enter a base: 5
Digit list is []
Digit sum is 0
String Rep is 0
Enter a string rep of a num with base 5: 3
The number is 3

Answer 1

Short Summary:

• Provided the source code and sample output as per the requirements.

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Source Code:

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
if base < 2 or num <= 0:
return []
  
if num == 0:
return num_to_digit_rec(num//base, base) + [num%base]

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
"""
numList = num_to_digit_rec(num,base)
total =0
for ele in range(0, len(numList)):
total = total + numList[ele]
# Write your code here
return total

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
if num < base:
return digits[num]
else:
return digit_str(num//base,base) + digits[num%base]

def uses_only(word, letters):
"""
Return True if word only uses characters from letters;
otherwise return False
"""
# Write your code here
for character in word:
if character == letters:
return True
else:
return False

def 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
if not uses_only(rep,digits):
return (int(rep,base))
  
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()

Refer the following screenshots for code indentation:

Sample Run:

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