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I am writing a Python program. Let me know if you want the program in some other programming language.

#definition of function d2x which takes two parameters v: which is a non #negative integer and x which is an integer between 2 and 9. this method #returns string of digits that represents the base-x representation of v

def d2x(v,x):

   remainder = v%x  

   if v<=1:

       return str(v)

   else:

       return str(d2x(v//x,x)) + str(remainder)

v= int(input("Enter a non negative integer: "))

x= int(input("Enter an integer between 2 and 9: "))

print(d2x(v,x))

Explanation:

I will explain the code line by line.

def d2x(v,x) This is the definition of function d2x which takes two parameters v: which is a non negative integer and x which is an integer between 2 and 9. This method returns string of digits that represents the base-x representation of v.

Now lets take an example to understand the working of this function.

Suppose the value of v = 10 and x = 2.

remainder = v%x  takes the mod of v and x which returns the remainder of the division of v by x. So v%x = 10 % 2 = 0. So remainder = 0.

if v<=1 This if condition checks if the value of v is less than or equal to 1. This is false because v=10 and 10 is greater than 1. If v is 1 or less than return str(v)  will return the value of v as it is i.e. 10.

Since the IF condition is false so the else part will execute which has the following statement: return str(d2x(v//x,x)) + str(remainder)

This calls the d2x function recursively. Here v is divided by x successively until the quotient of v divided by x is 0. On each successive division, the remainder is the new most significant digit. In v//x, the double slash is called floor division or integer division which we use as both v and x are integers. So using recursion the above statement becomes:

str(d2x(v//x,x)) + str(remainder)

str(d2x(10//2,2) + str(0)

d2x(5,2) + (0)

Now d2x will again be called recursively to perform the division and this successive division continues until quotient of v divided by x is 0. Here str() method is used returns the result in the form of string.  So v%x is the number which is added to the end of resultant number. v//x is the recursive portion which keeps using the answer of the previous binary number. This means 10 in base 2 calls convert(5,2), then adds 0 at the end. So when v//x=5 and v%x=0 So the answer is 1010.

At the end v= int(input("Enter a non negative integer: "))

x= int(input("Enter an integer between 2 and 9: "))  these two statement wills take integer input from user and print(d2x(v,x)) calls d2x method and print the result.