Section 7.4

Learning Goals

• DAT-1.C.a: Students will calculate the binary equivalent of a positive integer (base 10) and vice versa.

• DAT-1.A: Students will explain how data can be represented using bits. 

• Students will demonstrate that binary (base 2) uses only combinations of the digits 0 and 1.

• Students will demonstrate that decimal (base 10) uses only combinations of the digits 0 - 9.

• DAT-1: The way a computer represents data internally is different from the way the data are interpreted and displayed for the user. Programs are used to translate data into a representation more easily understood by people.

• DAT-1.C: For binary numbers:

• a. Calculate the binary (base 2) equivalent of a positive integer (base 10) and vice versa.

• b. Compare and order binary numbers.

• DAT-1.C.1: Number bases, including binary and decimal, are used to represent data.

• DAT-1.C.2: Binary (base 2) uses only combinations of the digits zero and one.

• DAT-1.C.3: Decimal (base 10) uses only combinations of the digits 0 – 9.

Objectives and General Description

The objective of this lesson is to introduce the students to the idea that computers operate in binary, which means that they store data and perform calculations using only zeros and ones ( Techterms.com) .  Students will also learn to perform basic binary/decimal conversions.

The lesson begins with a discussion activity to determine what students think binary is and how it relates to computing.  The next activity is a group demonstration that will showcase how the binary system represents decimal values and will enable students to discover the patterns that emerge when converting from decimal (base 10)  to binary (base 2).  Finally, each student will create a binary - decimal converter tool that will be used several times during the course.

Activities

Activity 7.4.1  (Budget 15 minutes)

1. In this activity, students will be introduced to the binary number system.  Pose the following question "What do 0's and 1's have to do with computing?".  Allow students 2 - 3 minutes to respond through small discussions, collaborative platforms like Padlet, google docs, or on sticky notes.  Either through this discussion or teacher input, students should learn that all data collected by a computer ultimately gets represented by zeros or ones.  This is a very abstract concept so students may not have an deep understanding of this but keep in mind that this is an introductory activity.  We will revisit the concept in our data unit.

2. Students will demonstrate the correlation between the decimal system and the binary system.  This activity is based off of "Count the Dots" by CS Unplugged.org.  The teacher should have printed a set of number cards (sample of cards).   Ask four students to come forward to demonstrate.  Each student is given a card.  Students should line up in order (card with one dot is on the right; card with the most dots is on the left).  Explain that you want the students to stand up and raise their card to represent a given number.  For example, who would stand up if I wanted to represent the value of 1?  The student who is holding the card that has one dot on it.  Go through several more examples.  Who would stand up if I wanted to represent the value of 3?  The student whose card has two dots and the student whose card has one dot.  Once the students understand the process, tell them that you want to count to 16.  Every time you say a number, the appropriate students stand up.  Students will begin to see a pattern emerge.  What happens when you get to 16?  There aren't enough cards.  Pose the question to the class..."What do we need to represent a higher number?"  They should decide that you need another card.

3. Do this same activity one more time.  However, this time write two columns of numbers on the board.  Once column is the decimal value that you are calling out.  The second column will be the binary equivalent of that value.  1's are used when a student stands up.  0's are used if the student is sitting down.  Start calling out with the value of 0 and go up to 10.  The students will begin to see the same pattern (stand up, sit down, etc.), matches the pattern of 1's and 0's to represent a decimal value.  Explain that this is a conversion chart between decimal values and their equivalent binary value.

Activity 7.4.2  (Budget 30 minutes)

Students will create a binary/decimal conversion tool called a Binary Flippy Do.  Each student will need a copy of the Binary Flippy Do Template, a pair of scissors and a marker.  Instruct the students to...

1. Fill in the top row, from RIGHT to LEFT, with base two exponents.  Start with 2^0 thru 2^7.  See the example of a completed Flippy Do.

2. Fill in the second row with the decimal equivalent of each of the corresponding base 2 exponent.

3. Fill in the third row with all zeros.

4. Trim the edges and cut on the dotted lines.

5. By trimming the dotted lines, the students have created flaps.  Fold each flap up and write a one on the back of each flap.

6. If possible, have a flippy do created on a large piece of poster board for the teacher to use for demonstrations.

7. Demonstrate how the flippy do works.  As the students what numbers on row two would add up to be a value of five.  The answer is a four and a one.  Tell them to flip up the flaps for the four and the one so that the "1" shows on the flippy do for each of those values.  Now when you read the flippy do, you should have 0 0 0 0 0 1 0 1.    You can then explain that a decimal value of 5 converts to a binary value of 101.  Give a few more practice problems for the students to complete.

8. Now demonstrate how to reverse the process.  Give them a binary value and ask them what the decimal equivalent is.  Students should flip up the flaps to represent the given binary value and then add up the decimal components represented by the "1"s to get the total decimal equivalent.  Try a few practice problems.

9.  Have each student create two binary/decimal conversion problems with answers.  Use these as bell ringers or quiz questions.

10.  Ticket out the door:  Have students explain how data can be represented using bits.

Resources

• 7.4.1: Count the Dots" by CSUnplugged.org (teacher resource)

• 7.4.1: Sample "Count the Dots" cards (student resource)

• 7.4.2: Binary Flippy Do Template (student resource)

• 7.4.2: Binary Flippy Do Template KEY (teacher resource)