How Can You Build a Majority Vote Counting Machine Using Only NAND Gates?

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Discussion Overview

The discussion revolves around designing a majority vote counting machine using only NAND gates, specifically for four input votes. Participants explore the application of Boolean logic and circuit design principles to achieve this goal.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant presents the algebraic solution for majority voting as ABC + ABD + ACD + BCD, indicating a need for two OR gates to combine results.
  • Another participant questions whether the problem allows for only 2-input NAND gates and discusses the possibility of using two levels of AND-OR logic.
  • Some participants express uncertainty about the application of two-level logic and request clarification on how to implement the design using NAND gates.
  • There is a suggestion to consider the inverted function for potential optimization in the design process.
  • Participants are encouraged to share their initial truth tables and logic implementations to further the discussion.

Areas of Agreement / Disagreement

Participants generally agree on the requirement to use NAND gates and the need for a majority vote counting mechanism. However, there is disagreement and uncertainty regarding the specific implementation details, such as the use of two-level logic and the constraints on gate types.

Contextual Notes

Participants have not yet provided complete truth tables or initial logic implementations, which may limit the clarity of the proposed solutions. There is also a lack of consensus on the constraints regarding gate types and configurations.

Who May Find This Useful

This discussion may be useful for students and practitioners interested in digital logic design, particularly those focusing on circuit construction using NAND gates and Boolean algebra.

daskywalker
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Homework Statement



Using NAND, AND OR, &/or NOR gates build a vote counting machine. It should light an LED when majority votes are true (or answer "yes"). Assume 4 input votes only.


Homework Equations



Boolean Logic

The Attempt at a Solution



So I know the solution in terms of algebra, which is ABC + ABD + ACD + BCD (where ABCD are the 4 input votes) and I know at the end I need two OR gates summing up to one single OR gate. Not sure how to design the beginning though.

I am also looking for a way to simplify it since I have to build the whole thing out of NAND gates only.
 
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daskywalker said:

Homework Statement



Using NAND, AND OR, &/or NOR gates build a vote counting machine. It should light an LED when majority votes are true (or answer "yes"). Assume 4 input votes only.


Homework Equations



Boolean Logic

The Attempt at a Solution



So I know the solution in terms of algebra, which is ABC + ABD + ACD + BCD (where ABCD are the 4 input votes) and I know at the end I need two OR gates summing up to one single OR gate. Not sure how to design the beginning though.

I am also looking for a way to simplify it since I have to build the whole thing out of NAND gates only.

Your problem statement doesn't confine you to 2-input gates. It only takes two levels of logic to do it with AND-OR logic, right?

Are you constrained to only using 2-input NANDs for the final circuit? How do you make an OR out of a NAND? Have you looked at the inverted function in case it offers some optimization? Please show us more work...
 
Yeah we can have 4 inputs, but I am still not sure about you saying using the two level AND-OR logic.
I know how to construct the different kind of gates from NAND gates now, just need a clear concept how to solve this problem.
 
daskywalker said:
Yeah we can have 4 inputs, but I am still not sure about you saying using the two level AND-OR logic.
I know how to construct the different kind of gates from NAND gates now, just need a clear concept how to solve this problem.

Show us your initial truth table and initial logic implementation.
 

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