Convert Decimal Number to Binary or Hex Without itoa function

#include <stdio.h>
#include <stdint.h>

void print_base(uint16_t num, uint8_t base) {
    // Your logic here

    int i = 0;
    char buf[20];
    char digit[20] = "0123456789ABCDEF";

    if(num == 0){
        printf("0");
        return;
    }
    while(num > 0){
    //     int rem = num % base;
    //     if(rem < 10){
    //         buf[i] = rem + '0';
    //     }else{
    //         buf[i] = 'A' + (rem -10);
    //     }
    //     i++;
    //     num = num /base;
            buf[i++] = digit[num % base];
            num = num / base;

     }

   for (int j = i - 1; j >= 0; j--) {
        putchar(buf[j]);
    }
}

int main() {
    uint16_t num;
    uint8_t base;
    scanf("%hu %hhu", &num, &base);

    print_base(num, base);
    return 0;
}