Dear Grandma,

This year I am in a class called Digital Electronics. I just recently finished the “Majority Vote project.” I was tasked with building a machine that will give “pass” or “fail” of a decision based on four votes: P for president, V for vice president, S for secretary, and T for treasurer. It needed to pass if a majority (3 or more votes of “yes”) was the case, or in the case of a tie, if the president voted yes, it also needed to pass. First, I constructed a truth table, which shows all the possible outcomes with, in this case, a 1 for a yes vote, and a 0 for a no vote. Generally in electronics, 1 means on and 0 means off. After I listed the possible outcomes, I analyzed the table and marked each of the scenarios that would produce a passing vote. I then wrote each of the cases in a logic expression. This consists of the letters representing the officers, i.e. PVST is a yes vote for all the officers. When you see P, or not P, it means that the vote of the president was a no. Using the logic expression, I proceeded to construct an electric circuit that worked for our voting constraints. The idea would be that each officer votes and the components in the circuit would take the electric pulses coming from the votes, depending yes or no, and give an output of pass or fail based on the scenario. To do this, I used AND, OR, and Inverter gates. An AND gate has two inputs that must be satisfied in order for an output to be given. An OR gate has two inputs, or which at least one must be satisfied in order for there to be an output. An Inverter takes the input value and flips it to be the opposite, so if the input was 1, the output would be 0. Once I had drawn up my circuit, I created a virtual model of it on the computer. This allows me to simulate outcomes. My circuit contained 24 AND gates, 7 OR gates, and 4 Inverter gates. Having many gates like this makes the circuit large and confusing, as well as costly to produce in real life. I used a nifty mathematical resource called Boolean algebra, which consists of several laws and theorems, to simplify my logic expression. The expression had 8 terms in it to begin with, but once I had simplified it, there were only 4 terms. I drew up a simplified circuit, and modeled it on the computer. This circuit only had 6 AND gates, 3 OR gates, and 1 inverter gate. This was a great improvement. After I had made a digital version of my circuit, it was time to build a real life prototype with a breadboard, which is a board that you can use to easily insert and replace electrical components in order to make a temporary circuit for testing. I quickly wired up my circuit and tested all of the inputs that should produce a passing output. I was successful on the first try. Then I proudly got my picture made with my circuit and added the picture to my portfolio of work for the class. I’m really enjoying this class. Can’t wait to see you over Thanksgiving break!

Your grandson,

Al