Applying Shannons Expansion Theorem

[shamieh]

Wasn't exactly sure where to post this. Wanted to see if I did this correctly.Can someone check my work please?

Problem: Consider f defined below. Apply Shannon's expansion theorem (also given below) with respect to input y as if you were implementing this function using a 2:1 MUX. Find the minimum equations for f(w,x,0,z) and f(w,x,1,z).
Shannons Expansion Theorem
f(w_1, w_2,...,w_n) = ~w_1 * f(0,w_2,...,w_n) + w_1 * f(1,w_2,...,w_n)

The function to be expanded: f(w,x,y,z) = wy + ~w~x~y + ~w~y~z + wy~z
Here is what I got for my solution.

~y(~w~x + ~w~z + ~wz) + y(w + w~z)

 

[Evgeny.Makarov]

Why do you have the term ~wz in the first part, the one that corresponds to y = 0?

 

[shamieh]

After re-doing the problem I obtained this: ~y(~w~x + ~w~z) + y(w + w~z)

 

[Evgeny.Makarov]

That's correct.

 

[LudusRex]

For f(w,x,0,z):
~0(~w~x + ~w~z + ~wz) + 0(w + w~z)
= (~w~x + ~w~z + ~wz)

For f(w,x,1,z):
~1(~w~x + ~w~z + ~wz) + 1(w + w~z)
= (w + w~z)