In your conversion function, for example, you do a modulo (%).
The result of the modulo is the converted "digit" which is obviously a number.
In your conversionGreater function, as you point out, sometimes the modulo returns a number > 9, which you correctly recognize as being a letter, not a number. But you have an array of ints, and you can't really store letters there.
So what I'm saying is to change your array of ints to an array of chars.
Make the string I mentioned above. Now the th index into the string is the character '0', the st index is '1', and so forth. The th index is 'a', which is the character that you want to print if the result of the modulo is 10.
So each time you perform the modulo, you'll get a number between 0 and (base-1). Use that number to index into the string to find the character you need to print.