Why are multiple increments/decrements valid in C++ but not in C?

test.(c/cpp)

#include <stdio.h>

int main(int argc, char** argv)
{
  int a = 0, b = 0;
  printf("a = %d, b = %d\n", a, b);
  b = (++a)--;
  printf("a = %d, b = %d\n", a, b);

  return 0;
}

If I save the above as a .cpp file, it compiles and outputs this upon execution:

a = 0, b = 0
a = 0, b = 1

However, if I save it as a .c file, I get the following error:

test.c:7:12: error: lvalue required as decrement operator.

Shouldn't the (++a) operation be resolved before the (newValue)-- operation? Does anyone have any insight on this?