Why is xor not universal

Community Bot 1 1 1 silver badge. Mitch Wheat Mitch Wheat k 42 42 gold badges silver badges bronze badges. I noticed you indented the middle part of your answer. Is this a quote from something, and if so, where? Keith K Keith K 1. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.

Email Required, but never shown. The Overflow Blog. Podcast Explaining the semiconductor shortage, and how it might end. Does ES6 make JavaScript frameworks obsolete? Featured on Meta. Now live: A fully responsive profile. XOR is commutative. First, a random key is generated. Then, XOR operation is performed using the key so that an encrypted data is created. In order to decrypt, the same key should be used and XOR operation should be run again.

We will present a proof based on parity that XOR is not universal. An XOR function that has its output without property E has exactly one of its two inputs with property E and one without. Why XOR gate is called an inverter? When one input is true, the output is the inversion of the other. When one input is false, the output is the non-inversion of the other. Helpful tips. What is XOR example? How is XOR calculated? The same is true for a circuit constructed entirely of XOR gates.

This is interesting, as I realise that a universal gate must be able to produce an output of 1 from 0 inputs. Thus, the only possible remaining candidate for a universal gates is XNOR. I didn't try this any further, but this could be experimented with on a circuit board.

Therefore you could go on forever and never get a NAND from any of these, therefore they are not universal. Clearly NOT is not universal since it only takes a single input. NOR is universal. However, it does make sense to have three-or-more-input gates for all of these logical gates except NOT. And for example a three-input XOR can be converted to a two-input XOR by setting one of the inputs to logical 0, so this hugely increases the possibilities.