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"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.

__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."__

**One way of seeing this is to note that applying an XOR gate does not change the total parity of the bits.**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.