Convert Decimal Number to Binary or Hex Without itoa function

Code

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

char hexchar[16] = {'0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F'};

void print_base(uint16_t num, uint8_t base) {
    uint16_t mask;
    switch (base) {
        case 2:
            mask = (1 << 15);
            if (!num) {
                printf("0");
                break;
            }
            while (!(num & mask))
                mask >>= 1;
            while (mask) {
                printf("%c", ((num & mask) ? '1' : '0'));
                mask >>= 1;
            }
            break;
        case 16:
            mask = (1 << 4) - 1;
            printf("%c", hexchar[(num >> 4) & mask]);
            printf("%c", hexchar[(num >> 0) & mask]);
            break;
        default:
            break;
    }
}

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

    print_base(num, base);
    return 0;
}

Solving Approach