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.