# Boolean Logic design help

## 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.

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.

Mentor

## 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.

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...