# All 16 Boolean Logic Gates

I was doing some reseach and I came across a website that had listed 16 different boolean logic operators. I was wondering if all of them were real, and if so, what do they do.

https://www.researchgate.net/figure/Method-for-implementing-all-16-Boolean-logic-functions-in-a-single-MR-unit-with-a_fig1_303770111

• If you consider functions that take two bits as input and one bit as output, you get of course $2^{2^2} = 16$ different functions and hence, you could possibly have $16$ possible gates for circuits. I guess it depends on the use case whether one actually build those for electrical circuits but in theory they of course exist. – ttnick Oct 29 '19 at 8:36

What do you mean by real? You can define as many logic gates as you want and build them. However, in a boolean logic with 2 inputs, there are 16 different combination of outputs. On the other hand, it proven that $$\{AND,NOT\}$$, $$\{OR,NOT\}$$, $$\{NAND\}$$ and $$\{NOR\}$$ are functionally complete (which means we can build all other combination from 16 outputs with only using gates in those sets ).