DE Unit 5
The Birthday Problem
The Birthday Problem Introduction

Welcome to Unit 5

Welcome to the 5th unit of Digital Electronics! By now, we’ve seen all the steps of the Circuit Design Process.  Using this process it’s possible to turn real-world problems, questions, or scenarios into actual working digital circuits.  Throughout the semester we’ve covered the different steps of the circuit design process, and they go like this:

  • Define inputs & outputs
  • Create a truth table
  • Create an unsimplified logic expression
  • Use Boolean algebra or a K-Map to simplify the expression
  • Create an AOI circuit by hand
  • Convert any parts of the circuit to NAND/NOR as needed
  • Simulate in Multisim
  • Add proper displays or display drivers
  • Breadboard!

This process will all come together in this unit into one giant problem: The Birthday Problem.  The completion of this circuit will give us a solid overview of the whole process, and also launch us into our next concept: the Programmable Logic Device (PLD). At the end of the unit, you will have reviewed and practiced the Circuit Design process in its entirety. You’ll also be ready for the next topic: PLDs.

Part 1: Review

Example Truth Table Setups

Example K-Map Setups

The first part of this unit asks you to go back and review some of the key ideas from the semester.  We’ll go back as far as AOI logic and NAND/NOR logic, as well as reviewing things like truth tables, K-Mapping, counting in binary, and even 7-segment displays.  It’s important to revisit each of these ideas briefly before the full Birthday Problem because each of those steps in the circuit design process will play a major role in the success of next project.  As you review these ideas, be sure to take a few pages of good notes as you think through those earlier topics from your new vantage point!


 Think about the circuits you’ve designed and built this semester.  Things like the Fireplace Circuit, Majority Vote, and Seatbelt Circuit. T ake a page of notes describing what you see as being the steps of the Circuit Design process.  Make yourself a cool and complete graphic organizer that outlines the main steps!

 Watch the four presentation on Displays, Binary, Truth tables, and the “Top Secret Pro Tool” (sshhh… don’t tell anyone!).  Take a full page of notes on these ideas.

Watch the four presentation on K-Maps, AOI, NAND, and NOR.  Take a full page of notes on these ideas.

 Have Mr. Benshoof approve your notes.

Seven Segment Displays

Counting in Binary

Truth Tables

(Top Secret Pro Tool)


AOI Circuit Design

NOR Logic

Part 2: Plan, Simulate & Build

Boolean Algebra Equations

 Download the Part 2 Rubric Only

 Take the Unit 2 Quiz

Our second part to the unit covers how to convert our logic expressions into actual circuit diagrams.  To do this, we’ll emphasize on how mathematical notation for multiplying and adding turns into the “Ands” and “Ors” or AOI logic.  We’ll also look at some Boolean Algebra rules that let us simplify logic expressions before making circuits.


 Take a full page of good notes on AOI Implementation.  Make sure to emphasize when each of the three gates (And/Or/Inverter) are used!

 Complete the AOI Implementation Assignment.

 Use Multisim to simulate and then breadboard the required circuits from the AOI Implementation Assignment.

 Take a full page of careful notes on Simplifying Expressions - be sure to emphasize the different rules for simplifying.

 Complete the Simplifying Expressions Assignment.

  Take the Unit 2 Quiz: AOI Design!

 Have Mr. Benshoof check-off your notes, assignments, and circuits.

AOI Implementation

Simplifying Expressions

Simplification Overview

Part 3: PLDs

PLD Overview

Our unit ends with a short project that has you work through the entire circuit design process in the creation of a solution to a small problem. In this “Majority Vote” problem, you’ll be asked to create a circuit that can tally votes for a small group of people following a specific set of criteria. You’ll need to start by creating a truth table from the problem situation, then writing an AOI logic expression and simplifying if possible. You’ll then convert your expression into a hand-drawn circuit, a Multisim simulation, and finally a breadboarded model.


 Read through the Majority Vote problem carefully and watch the overview video.

 Create a Truth Table that describes the situation in your engineering notebook.

 Write an unsimplified logic expression from your truth table.

 Simplify your logic expression to get a final simplified logic expression.

 Have Mr. Benshoof confirm your simplified logic expression.

 Draw an AOI circuit diagram from your simplified logic expression

 Simulate your AOI circuit in Multisim

 Breadboard your AOI circuit and confirm that it works

 Have Mr. Benshoof confirm your working breadboard circuit.

DE Unit 5 Map
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