# Shannons Theorem Expansion Problem

Discussion in 'Homework Help' started by Shamieh, Mar 14, 2014.

1. ### Shamieh Thread Starter Member

Oct 24, 2013
36
1
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) + y(w + w~z)

Last edited: Mar 16, 2014
2. ### panic mode Senior Member

Oct 10, 2011
1,328
305
not sure i understand your notation but assuming tilda means next char is inverted then:

f(w,x,y,z) = wy + ~w~x~y + ~w~y~z + wy~z

therefore:
f(w,x,0,z) = w0 + ~w~x~0 + ~w~0~z + w0~z
f(w,x,0,z) = 0 + ~w~x + ~w~z + 0
f(w,x,0,z) = ~w~x + ~w~z

f(w,x,1,z) = w*1 + ~w~x~1 + ~w~1~z + w1~z
f(w,x,1,z) = w + ~w~x*0 + ~w*0~z + w~z
f(w,x,1,z) = w + 0 +0 + w~z
f(w,x,1,z) = w +w~z

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