Core Java. Improving algorithm ( get rid of switch-case statement )

I need to map real number to another numer system ( from 2 to 16 ).
Like this one http://planetcalc.com/862/ 
 I come up with solution below. However, I need to make further improvement of the algorithm. Particularly speaking, I need to get rid of switch-case statement when I map letters. I feel that the solution will be through ASCII table ( http://www.ascii-code.com/ ) . Please tell how to elegant version of the solution will be look like ( I probably should work thought StringBuilder if so what method best to use ) . Thx in advance !

public class Task {
    public static void main(String[] args) {
        int number = 1289;
        int N = 2; // radix = 2...16

        if (N < 2 && N > 16) {
            System.out.println("Radix is out of bounds");
            return;
        }
        if (number < 0) {
            System.out.println("Number is not natural");
            return;
        }
        if (number == 0) {
            System.out.println("0");
            return;
        }
        System.out.println(trans(number, N));
    }

    public static String trans(int num, int N) {
        if (num == 0) {
            return "";
        }

        String str;
        switch (num % N) {
            case 10:
                str = "A";
                break;
            case 11:
                str = "B";
                break;
            case 12:
                str = "C";
                break;
            case 13:
                str = "D";
                break;
            case 14:
                str = "E";
                break;
            case 15:
                str = "F";
                break;
            default:
                str = String.valueOf(num % N);
        }
        return trans(num/N, N) + str;
    }
}

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