You can distinguish full and empty using x-y=0 vs x-y=N if the length N is a power of two and smaller than the integer type holding indices x, y. No unused element needed then.
The trick with powers of two is that you can just look at the MSB of `x XOR y` where x and y have one more bit than necessary to store the size.
So for instance if you have a buffer with 8 entries you have a read pointer and a write pointer, both wrapping at 16 (4bits). When you address the buffer you ignore the MSB, when you want to test for empty you do `read == write`, when you want to test for full you do `read XOR write == 0b1000`.
So you only have extremely cheap comparisons, bitwise XOR and counter increments to implement all operations.
