This exercise is supposed to be of medium difficulty, but this is the solution proposed by the mentor:

public static Number convertNumberToOtherNumberSystem(Number number, NumberSystem expectedNumberSystem) {
     checkDataIsValid(number);
     BigInteger result = to10NumberSystem(number);
     return from10TOExpectedNumberSystem(result, expectedNumberSystem);
 }

 private static Number from10TOExpectedNumberSystem(BigInteger number, NumberSystem expectedNumberSystem) {
     if (NumberSystemType._10.equals(expectedNumberSystem)) {
         return new Number(expectedNumberSystem, number.toString());
     } else {
         BigInteger divider = new BigInteger("" + expectedNumberSystem.getNumberSystemIntValue());
         BigInteger dividend = new BigInteger(number.toString());
         String result = "";
         //number is current
         while (dividend.compareTo(BigInteger.ZERO) > 0) {
             BigInteger integer = dividend.divide(divider);
             String s = dividend.subtract(integer.multiply(divider)).toString();
             result = (s.length() == 1 ? s : getChar(s)) + result;
             dividend = integer;
         }
         return new Number(expectedNumberSystem, result);
     }
 }

 private static String getChar(String s) {
     return "" + (char) (Integer.parseInt(s) + 87);
 }

 private static void checkDataIsValid(Number number) {
     if (number.getNumberSystem().getNumberSystemIntValue() <= 10) {
         checkDigitsLimited(number.getDigit(), number.getNumberSystem().getNumberSystemIntValue() + 48);
     } else {
         checkCharsLimited(number.getDigit(), number.getNumberSystem().getNumberSystemIntValue() + 87);
     }
 }

 private static void checkCharsLimited(String digit, int value) {
     for (char c : digit.toCharArray()) {
         if (!(c >= 48 && c <= 57) && !(c >= 97 && c < value)) {
             throw new NumberFormatException();
         }
     }

 }

 private static void checkDigitsLimited(String digit, int value) {
     for (char c : digit.toCharArray()) {
         if (!(c >= 48 && c < value)) {
             throw new NumberFormatException();
         }
     }
 }

 private static BigInteger to10NumberSystem(Number number) {
     BigInteger result;
     if (NumberSystemType._10.equals(number.getNumberSystem())) {
         result = new BigInteger(number.getDigit());
     } else {
         result = BigInteger.ZERO;
         char[] digits = number.getDigit().toLowerCase().toCharArray();

         //to _10 number system
         BigInteger power = new BigInteger("" + number.getNumberSystem().getNumberSystemIntValue());
         BigInteger multiplier = BigInteger.ONE;

         for (int i = digits.length - 1; i >= 0; i--) {
             result = result.add(multiplier.multiply(getData(digits[i])));
             multiplier = multiplier.multiply(power);
         }

     }
     return result;
 }

 private static BigInteger getData(char c) {
     if (c >= '1' && c <= '9' || c == '0')
         return new BigInteger("" + c);
     else return new BigInteger("" + (c - 87));
 }