Overwrite a string in C

I am new to programming and I'm trying to create a code that converts a decimal into any base between 2 and 16. But I don't know how to write in a new value in my string.

void base_conversion(char s[], int x, int b) {
int j, y;
j = 0;
// your code here
while(b > 1 && b < 17) {

    if (x < 0) {
        x = (-x);
    }else if(x == 0) {
        s[j] = '\0';
    }
        x = (x/b);

    while(x > 0) {

        y = (x%b);


        if (y == 10) {
            s[j] = 'A';
        }else if(y == 11) {
            s[j] = 'B';
        }else if(y == 12) {
            s[j] = 'C';
        }else if(y == 13) {
            s[j] = 'D';
        }else if(y == 14) {
            s[j] = 'E';
        }else if(y == 15) {
            s[j] = 'F';
        }else{
            s[j] = y;
        }
    }
}j = j + 1;
}