Unit Objective: This unit is designed to introduce the concepts of binary and hexadecimal systems. Although the activities were written for an Algebra 1 course, they could easily be adapted for other courses.

Activity 1: Four Person Counting Activity

Objective: Students will use a hands-on activity to introduce counting with binary and also learn about place value.

Wyoming Standards:    Math 1.1-Students represent and apply real numbers in a variety of forms.
Math 1.2-Students apply the structure and properties of the real number system.

Materials Needed: Scratch paper, tape or sticky tack.

Time: 20 minutes

Directions: Before the activity begins write the numbers 1, 2, 4, 8, and 16 using large numerals on a pieces of scratch paper. Next ask for three student volunteers. They will be used to help you count. Give the student volunteers the numbers 1, 4, and 8 (keep 2 and 16 for yourself). Arrange the students and teacher in a line from left to right in order from greatest to least starting with 8 (8, 4, 2, 1). Since the teacher is holding the 2, he or she will be third in line.

Explain to the class that the line of volunteers will be doing a counting exercise. The volunteer can only say their number or can combine with other volunteers to create a new number by addition. First volunteer 1 will say “One” while holding up the number 1. Next volunteer 2 (the teacher) will say “Two” while holding up the number 2. Since there is not a volunteer 3, volunteers 1 and 2 will have to combine to say “Three”. They should say “Three” together while they both hold up their numbers. Continue this until you finally reach 15.

Next ask the students how to make a 16. When one of the students declares a volunteer to hold 16 would be necessary, have that student come up to the front and stand to the left of volunteer 8. Give this student the paper with 16 on it. Start the counting process over starting at 1 again. It should go much faster now.

When the group reaches 32 ask the students how to make the next number. They will state “We need someone to hold 32!” At that point they have a basic understanding of binary place value. You can then have the volunteers return to their desks. Collect the numbers 1, 2, 4, 8, and 16.

Use the tape or sticky tack to hang the numbers on the board in the same order as the line of volunteers. Show how “1” is in the units place which equals 20. Write 20 underneath the “1”.
Show how “2” is in the two's place which equals 21. Write 21 underneath the “2”.
Show how “4” is in the four's place which equals 22 or 2x2. Write 22 and 2x2 underneath the “4”.
Continue doing this for the “8” and “16”. Ask the students what will be next. They should be able to figure out that 32 (25) and 64 (26) will be next.

Finally you can have the students write binary numbers. On the board the teacher should write 0001 binary =1, 0010 binary=2, 0011binary=3, 0100 binary=4, etc. Students should copy these into their notebooks.

Activity 2: How We Talk to Machines

Objective: The students will review and use binary numbers to introduce the idea of hexadecimal numbers.

Wyoming Standards:    Math 1.1-Students represent and apply real numbers in a variety of forms.
Math 1.2-Students apply the structure and properties of the real number system.

Materials Needed: Computer with Internet access

Time: 20 minutes

Directions: Have the students access the Space Place web site. This can be done individually, in pairs, or as a group. The first part of the page is a review of binary numbers. Have the students do this review first. There is also a short binary quiz at the bottom of the web page. The students can also do this quiz. Do not have the students go on to the next web page yet. When everybody has completed the quiz the teacher may need to go over the results of the quiz to answer questions about binary.

Next have the class brainstorm ideas why we use a base 10 (decimal) system instead of a base 2 (binary) system. This is a good opportunity to compare and contrast the systems. A table or Venn diagram works well for this. One of the disadvantages of binary the students should see is the difficultly in writing larger numbers, like the number one hundred or one thousand. Point out that although it is difficult for humans to work with these types of binary numbers, machines work wonderfully with binary.

Have the students go back to the web site and proceed to the next page on hexadecimal. It is a good idea to read through this page together. Emphasize that hexadecimal number like A0A0 are fairly easy for humans to read and easy for machines to convert back to binary. It is a good idea to have the students update their notebooks from the previous lesson, adding hexadecimal values to their table. For example, 1010 binary=10 can be updated to 1010 binary=10=A hex. It will help to have these values on their table to convert hexadecimal to binary and binary to hexadecimal.