# 2.9. Binary Numbers¶

This lesson reinforces the enduring understanding that binary sequences can be used to represent all digital data through abstraction. Students learn how to convert numbers to and from different number base systems and that numbers may represent different types of data in different contexts. While this unit introduces the binary and other number systems, Unit 3 will take a more in-depth look at the hexadecimal system, including how it is used in computing.

### Professional Development

The Student Lesson: Complete the activities for Mobile CSP Unit 2 Lesson 2.9: Binary Numbers.

## 2.9.1. Learning Activities¶

### Estimated Length: 90 minutes

• Hook/Motivation (5 minutes): Show the joke on the t-shirt image (also at the beginning of the Mobile CSP lesson). The "10" on the T-shirt is using a different number base. In the binary number system, there are only 2 digits (0 and 1) so 10 has the value of 2. The decimal system is base-10 and has 10 digits (0, 1, 2, 3, ...9). That system is the one we normally use for numbers. So, the t-shirt really means there are only 2 types of people in the world; those who understand binary and those who don't. Another possible hook is to play the 2048 game and then ask them what is the sequence 2, 4, 8, 16, etc. (the powers of 2) and tell them we will use the powers of 2 to convert binary to decimal (base 10) numbers.
• Experiences and Explorations (80 minutes):
• Presentation: Using the slide deck (through slide 6) or by showing the video, go through the introduction of binary numbers.
• Discussion: Binary counting - watch the CS Unplugged video. We recommend that you act it out with your students, using Binary Dot Cards which you should print out before class. In this activity, only have them count up in binary. Bring back the cards later to do conversions.
• Activities: You may choose to have your students complete some or all of the activities in each section. Have students work jointly (either in pairs or small groups) to construct a binary odometer that counts to the decimal value of 20. Using paper and pencil, have the students write down the first 20 values of the binary number system starting with 0. You may choose to have the students do this activity by completing the Binary Column of this Base Conversion Worksheet.
• Explanation: Compare a decimal odometer (10 digits) with a binary odometer (2 digits). Students know how the decimal odometer works: It starts at 000. The rightmost column cycles through the digits 0 through 9 before the next digit to the left is incremented giving 010 (10 miles). For the binary odometer, the rightmost digit cycles from 0 though 1 before the next digit to the left is increment giving 10 (2 miles). The key point here is that in any number system, the wheel in the next column to the left doesn't turn until the wheel in the adjacent column (to the right) turns over to 0. In decimal, the 10s column doesn't turn from 0 to 1 until the 1s column turns from 9 to 0.
• Presentation: Using the slide deck (slide 7-20) or by showing the video, go through converting Binary to Decimal and Decimal to Binary.
• Also, point out that both binary and decimal odometers are positional number systems. Point out that numbers, including binary data, are represented by bits and are used to store digital data.
• Activities: You may have your students complete some or all of the activities listed in each section, but you should make sure that your students can convert numbers between binary (base 2) and decimal (base 10). We recommend that you use Binary Converter Tool (print double-sided and cut at dotted lines to make tabs of the 1's so they can be flipped backwards to cover the 0's) or the online binary converter tool and the Binary/Decimal Worksheet. If your class has time, have them explore the Maya Math Game (a base 20 number system) in pairs.
• Rethink, Reflect and/or Revise (5 minutes): The position number system pattern, base conversion worksheet, and interactive exercises. Discuss: Why do computers use binary?

### AP Classroom

The College Board's AP Classroom provides a question bank and Topic Questions. You may create a formative assessment quiz in AP Classroom, assign the quiz (a set of questions), and then review the results in class to identify and address any student misunderstandings.The following are suggested topic questions that you could assign once students have completed this lesson.

Suggested Topic Questions:

• Topic 2.1 Binary Numbers

## 2.9.2. Professional Development Reflection¶

Discuss the following questions with other teachers in your professional development program.

• How does this lesson help students toward the enduring understanding that a variety of abstractions built on binary sequences can be used to represent all digital data?

I am confident I can teach this lesson to my students.
• 1. Strongly Agree
• 2. Agree
• 3. Neutral
• 4. Agree
• 5. Disagree