Academic journal article The Science Teacher

# A Computer Story: Complexity from Simplicity: Understanding Electrical Circuits, Digital Systems, Truth Tables, and Base-N Number Systems

Academic journal article The Science Teacher

# A Computer Story: Complexity from Simplicity: Understanding Electrical Circuits, Digital Systems, Truth Tables, and Base-N Number Systems

## Article excerpt

In this technological age, digital devices are conspicuous examples of extraordinary complexity. When a user clicks on computer icons or presses calculator buttons, these devices channel electricity through a complex system of decision-making circuits. Yet, in spite of this remarkable complexity, the hearts of these devices are components that make simple decisions.

This article describes an activity in which students learn how complex outcomes can result from simple decisions. Participants encounter a broad range of learning experiences, including electric-circuit construction, household wiring, digital systems, truth tables, and the concept of base-n number systems. The activity culminates in a dramatic demonstration of complexity from simplicity: Each student becomes an element in a digital decoder, translating a binary number into its decimal counterpart, which then appears on an illuminated, seven-segment display.

Motivation, overview, and connections

We have run the "Complexity From Simplicity" program 18 times for a range of upper elementary through early high school science classes, nine of which were ninth-grade classes. The program seems to work best at the high school level; in this article, we describe the ninth-grade version used in the classroom of one of the authors, Amanda Weidenhammer. One teacher can teach this program, which takes about 90 minutes of class time, though it's easier with two adults.

The program is divided into four parts. The first activity, in which students construct electrical circuits, takes about 30 minutes, including introduction and instructions. Students work in pairs to construct simple, series, and parallel circuits.

Taken together, the two middle activities occupy about 25 minutes of class time. Here, the teacher works with the whole class to develop the basics of binary (base-2) logic and connect the ideas of student-constructed circuits, truth tables, and digital devices' logical operations.

In the last activity, students work individually with their own truth tables and as a class to develop a common class goal of becoming a human digital decoder. This final part of the program takes about 25 minutes.

Student writing opportunities exist before, during, and after the program. Students can record observational data and their analysis in a traditional lab notebook, construct KWL (what we Know, what we Want to know, what we Learned) charts, or participate in alternative reflection methods. We assess students based on pre- and postactivity questions, but these don't represent a comprehensive student examination or substitute for reflective writing.

Electrical circuit construction

We have run the circuit part of the "Complexity From Simplicity" program for about 20 years and over 100 times since 2004, involving over 2,000 students in grades 3-9. At the end of those programs, we commonly demonstrate series and parallel circuits as decision makers. Only more recently did we envision an extension that would carry students from simple electrical circuits and seemingly abstract mathematics to sophisticated artificial intelligence and decision-making devices.

Series and parallel circuits provide powerful illustrations of decision-making machines. There are four combinations of input settings--on-on, on-off, off-on, off-off--that use two switches to create specific lightbulb responses (i.e., on, off). To begin this activity, we divide students into pairs and provide each pair with a wiring diagram handout and a circuit kit (Figure 1). We show students how to use a screwdriver to fasten the forklike lugs, which are attached to the ends of some wires, under the loosened screws of household switches. We also instruct them in the use of wire nuts, explaining that these are used in household wiring.

We provide students with a handout of the simple circuit diagram shown in Figure 1 (p. 49) and, working in pairs, students construct the simple circuit. …

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