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) {
    bool start = false;
    if (base == 2) {
        for (int8_t i = 8-1; i >= 0; i--) {
            char val = (num & (1 << i)) ? '1' : '0';
            if ((val != '0' || i == 0) && start == false) {
                start = true;
            }

            if(start) {
                putchar(val);
            }
        }
    }else if (base == 16) {
        for (int i = 2 - 1; i>=0; i--) {
            uint8_t val = (num >> 4*i) & 0x0F;
            putchar((val >= 0 && val <= 9) ? (val + '0') : (val-10 + 'A'));
        }
    }
}

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

    print_base(num, base);
    return 0;
}

Solving Approach