addition of 2 unsigned int with bitwise operator in C

bitwise_add.c

#include <stdio.h>
// add with bitwise operators
unsigned int add_binary(unsigned int x, unsigned int y){
  unsigned int a = x ^ y;
  unsigned int b = (x & y);
  if (b == 0){
    return a;
    }
  else{
    b = b << 1;
    return add_binary(a, b);
  }
}

int main(){
  unsigned int a = 12;
  unsigned int b = 78;
  
  unsigned int c = add_binary(12, 78); // 90
}