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

[daskywalker]

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.

 

[berkeman]

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...

 

[daskywalker]

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.

 

[berkeman]

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.

 

[DeeNos]

I would suggest breaking down the problem into smaller parts and then combining them to create the final solution.

First, you can start by creating the basic logic for each individual vote. For example, using NAND gates, you can create a circuit that outputs a "yes" only when both A and B inputs are true.

Next, you can combine these individual logic circuits using AND gates to create a circuit that outputs a "yes" only when all four votes are true.

To simplify the circuit and use only NAND gates, you can use De Morgan's laws to convert the AND gates into NAND gates. This will help reduce the number of gates needed and make the circuit more efficient.

Finally, you can use an OR gate to combine the outputs of the individual vote circuits and the final AND gate circuit. This will result in an LED being lit when the majority of votes are true.

In summary, the solution using only NAND gates would involve breaking down the problem into smaller parts, using De Morgan's laws to simplify the circuit, and then combining the individual circuits to create the final vote counting machine.