Applying Shannons Expansion Theorem

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    Expansion Theorem
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Discussion Overview

The discussion focuses on the application of Shannon's expansion theorem in the context of a specific function defined over multiple variables. Participants are examining the correctness of a solution involving the implementation of this function using a 2:1 multiplexer (MUX). The scope includes mathematical reasoning and technical explanation related to Boolean functions.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant presents a function f(w,x,y,z) and applies Shannon's expansion theorem to derive expressions for f(w,x,0,z) and f(w,x,1,z).
  • Another participant questions the inclusion of the term ~wz in the expression corresponding to y = 0.
  • A subsequent reply indicates a revised solution that omits the questioned term, suggesting an adjustment in the approach.
  • One participant confirms the revised solution as correct.

Areas of Agreement / Disagreement

The discussion shows some disagreement regarding the initial solution, particularly concerning the inclusion of specific terms. However, there is agreement on the correctness of the revised solution presented later.

Contextual Notes

Participants have not explicitly stated all assumptions or dependencies related to the definitions used in the problem. The discussion does not resolve all potential ambiguities in the application of Shannon's theorem.

Who May Find This Useful

This discussion may be useful for students or practitioners interested in Boolean algebra, digital logic design, or those studying Shannon's expansion theorem and its applications in circuit design.

shamieh
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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)
 
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Why do you have the term ~wz in the first part, the one that corresponds to y = 0?
 
After re-doing the problem I obtained this: ~y(~w~x + ~w~z) + y(w + w~z)
 
Last edited:
That's correct.
 

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