Convert Decimal Number to Binary or Hex Without itoa function

Code

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

void binary(int num){
    if (num == 0) return;
    binary(num >> 1);
    printf("%d", num & 1);
}

void hex(int num){
    if (num == 0) return;
    hex(num >> 4);
    printf("%X", num & 0xF);
}

void print_base(uint16_t num, uint8_t base) {
    if (base == 2){
        if (num == 0){
            printf("0");
        }
        else{
        binary(num);
        }
    }
    else if (base == 16){
        hex(num);
    }


    // Your logic here
}

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

    print_base(num, base);
    return 0;
}

Solving Approach