# Is the 2 to 1 MUX universal?

Is the 2 to 1 multiplexer universal? Can it create a 7 to 1 multiplexer by multiplying its logic circuit?

It is not universal by itself. Here is how you can implement the AND and OR gates using it:

(I am going to use the more conventional notation - I.e. the s for the selector, d0 for the first data input and d1 for the second)

The general function of such a MUX is

f = s'.d0 + s.d1


If s=a, d0=a and d1=b you get

f = a'.a + a.b = a.b


Which is AND function.

If s=a, d0=b and d1=a you get

f = a'.b + a.a = a'.b + a = a + b


Which is the OR function.

There is no way to implement the NOT function though. But! if you can use constants in addition, then it becomes possible:

If s=a, d0=1 and d1=0 you get

f = s'.1 + s.0 = s'


Which is the NOT function.