The Arizona STEM Acceleration Project

The Half Adder

The Half Adder

A 7th Grade STEM Lesson

Jeff Ringer

June 2023

Notes for Teachers

This lesson builds on the previous lesson of Boolean operations and applies the concept of logic gates to build a one bit calculator - similar to Stibitz’ Model K which led to the first digital computer.

There is a readme file available with handouts.

The circuits can be built with a breadboard or simulator - the same components are used either way.

List of Materials

• Access to tinkercad.com or a breadboard
• Per Student
• A power source for breadboard
• A Resistor may be needed if power supply is too strong.
• 1 AND gate 74_008 IC
• 1 XOR gate 74_086 IC
• 1 OR gate 74_032 IC
• Two switches and two LED indicators
• Optional - snap circuits by Elenco SC-750R
• Handouts in the ReadMe file

Standards

ELA

7.RI.3

Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how individuals influence ideas or events)

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Mathematical Practices

1. Make sense of problems & persevere in solving them
2. Reason abstractly & quantitatively
3. Construct viable arguments & critique the reasoning of others
4. Model with mathematics
7. Look for & make use of structure

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Computer Science

7.CS.D.1 Identify some advantages, disadvantages, and consequences with the design of computer devices based on an analysis of how users interact with devices.

7.CS.T.1 Evaluate strategies to fix problems with computing devices and their components within a system.

Engineering Practices

Using Mathematics and Computational Thinking

Asking Questions and Defining Problems

Objective(s):

By the end of the lesson, you will be able to build a logic circuit for a half adder.

Agenda

Introduction with driving question and review of past learning.

Anticipatory activity - Students will be given circuits with AND and OR gates and asked how can the these gates be used to add one plus one.

Reading about Shannon and Stibitz

Reading on Boolean Truth tables for logic gates

Instruction on adding one plus one in binary.

Building the truth table for adding one and one.

Using the truth table to build a circuit.

Intro/Driving Question/Opening

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How do computers add numbers? How can electricity do arithmetic?

Hands-on Activity Instructions

• Group size can vary and may be limited by the amount of materials if using physical materials rather than virtual.
• Each student can do their own online and then in smaller groups use the breadboard to recreate the same circuit.
• Step-by-step directions will be in the readme.

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Assessment

Reading Assessment

1. What is a logic gate?

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1. What is a Truth Table?

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1. How might logic gates and truth table be used to create a circuit that can add two binary digits?

Engineering Assessment

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The SUM output comes on when only one switch is active and the Carry output comes on when both switches are active.

Differentiation

Students who struggle with the base two system will benefit from making the connection between base ten and base two explicit; review place values for both bases and have students draw a Venn diagram to show the differences and similarities of the two systems.

Students who struggle with wiring can review the basics of a circuit. PHET has a good simulator with lessons.

Remediation

Extension/Enrichment

Students that mastered the activity can learn how to draw the logic gates and draw a circuit diagram of the half adder.