Convert Decimal Number to Binary or Hex Without itoa function

Code

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

void print_base(uint16_t num, uint8_t base) {
  
    if(base == 2) {
        bool start_printing = false;
        for(int i = 15; i >= 0; i--) {
            int bit = (num >> i) & 1;
            if(bit == 1) {
                start_printing = true; 
            }
            if(start_printing) {
                printf("%d", bit);
            }
        }
        if(!start_printing) {
            
            printf("0");
        }
    } 
    else
    {
        printf("%X",num);
    }
    
}

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

    print_base(num, base);
    return 0;
}

Solving Approach