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
d1=b you get
f = a'.a + a.b = a.b
Which is AND function.
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:
d1=0 you get
f = s'.1 + s.0 = s'
Which is the NOT function.