Below is the extraction from quantum computer book, but I think my question is related to classical computing; "Now let us generalize from one to multiple qubits. Figure 1.6 shows five notable multiple bit classical gates, the AND, OR, XOR (exclusive-OR ), NAND and NOR gates. An important theoretical result is that any function on bits can be computed from the composition of NAND gates alone, which is thus known as a universal gate. By contrast, the XOR alone or even together with NOT is not universal. One way of seeing this is to note that applying an XOR gate does not change the total parity of the bits. As a result, any circuit involving only NOT and XOR gates will, if two inputs x and y have the same parity, give outputs with the same parity, restricting the class of functions which may be computed, and thus precluding universality." I searched over the dictionary and understood the meaning of universal gate, but I do not get the total parity of the bits. What does that mean? and what does that underlined, bold sentence imply? I searched, and I found parity bits, but it seems that it's little bit different from what I am looking for.