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) {
    if(num == 0){
        putchar('0');
        return;
    }
    if(base == 2){
        bool binState = false;
        for(int i = 15; i >= 0; i--){
            if(((num >> i) & 1U) || binState){
                binState = true;
                putchar(((num >> i) & 1U) + '0');
            }
        }
    }else if(base == 16){
        for(int i = 3; i >= 0; i--){
            uint8_t nibble = ((num >> (i * 4)) & 0x0F);
            if(nibble){
                putchar(nibble > 10 ? 'A' + nibble - 10 : '0' + nibble);
            }
        }
    }
}

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

    print_base(num, base);
    return 0;
}