My reaction is this, shift the argument right until it is zero, counting runs of zeros, noting the longest. I hope this is valid C++, I mostly write in C#.

int binary_gap ( unsigned n )
{
  int best_gap = 0;
  for ( int gap = 0; n != 0; n >>= 1 )
  {
    if ( ( n & 1 ) == 0 ) gap += 1;
    else 
    {
      if ( gap > best_gap ) best_gap = gap;
      gap = 0;
    }
  }
  return best_gap;
}

Your solution seems rather complicated. I suggest this: shift the argument right until it is zero, counting runs of zeros, noting the longest. I hope this is valid C++, I mostly write in C#.

int binary_gap ( unsigned n )
{
  int best_gap = 0;
  for ( int gap = 0; n != 0; n >>= 1 )
  {
    if ( ( n & 1 ) == 0 ) gap += 1;
    else 
    {
      if ( gap > best_gap ) best_gap = gap;
      gap = 0;
    }
  }
  return best_gap;
}