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
    if(num==0){
        printf("0");
        return;
    }
    switch(base){
        case 2:
            int start;
            for(int i = 15; i >= 0; i--){
                int bit = (num >> i) & 1;
                if(bit) start = 1;
                if(start) printf("%d",bit);
            }
            break;
        case 16:
            printf("%X",num);
            break;
    }
}

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

    print_base(num, base);
    return 0;
}