Calculating powers of 2, prints out 0 every time

Here's my code:

int foo() {
  int a = 1;
  while(1) {
    a *=  2;
    printf("a = %d\n", a);
  }
  return a;
}


int main(void) {
  foo();
  return 0;
}

It just keeps printing out "a = 0". I'm confused! Am I missing something really simple?