How can I implement this Truth Table with MUX4 only?
As you will see below, José was extremely close. Never give up!



Assuming X1:X0 (IN2:IN1) is the right hand multiplexer in José's diagram.

For RH mux input D0 selected:

X3  X2  X1  X0    Z(D0)
 0   0   0   0    1
 0   1   0   0    1
 1   0   0   0    1 
 1   1   0   0    x - choose x=1

Z=1 for all 4 entries!
We simply set RH mux D0 to 1, above four entries work.
José got RH D0 exactly right.
Four entries done, 12 to go!

Next up: RH Mux input D3 selected:

X3  X2  X1  X0    Z(D3)
 0   0   1   1    0
 0   1   1   1    0
 1   0   1   1    x - choose x=0
 1   1   1   1    x - choose x=0

Z=0 for all 4 entries!
We simply set RH Mux D3 to 0, above four entries also work.
José also did these 4 entries correctly.

8 Entries Done, 8 to go!


That was the easy half.  Now for a slightly harder challenge:

Show the last two remaining RH Mux input sets.
In the LEFT  column, X1:X0 selects input D2.
In the RIGHT column, X1:X0 selects input D1.

X3  X2  X1  X0  Z(D2) Z(D1) X3  X2  X1  X0
 0   0   1   0    0     0   0   0   0   1
 0   1   1   0    1     1   0   1   0   1
 1   0   1   0    x     1   1   0   0   1
 1   1   1   0    x     x   1   1   0   1

 If we choose x wisely we get the two sets to have identical outputs:

 0   0   1   0    0     0   0   0   0   1
 0   1   1   0    1     1   0   1   0   1
 1   0   1   0    1     1   1   0   0   1
 1   1   1   0    0     0   1   1   0   1


This means we can use exactly the same function for D1 &amp; D2 inputs on the RH mux.  

José correctly created this function using the left hand mux.

He also correctly connected the RH mux input D1 to the function.

All 16 table entries done, we are done!  

José, you were extremely close, good work :)