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Lesson: Bits & Binary

binary

Image from LaMenta3 on Flickr Commons

(Adapted from CSIRO, Australia’s Commonwealth Scientific and Industrial Research Organisation, and New Zealand’s Computer Science Unplugged, activities designed to teach the basics without computers.)

Summary

In this activity, students in grades 4 – 12 will do math like a computer. They will learn the basics of binary number systems by counting on their hands, and use their knowledge to decode numbers and letters.

Grade level: 4-12

Time: 45 minutes

Introduction

Computers are just one of many technologies that use the binary number system — zeros and ones — to convey information. All ‘digital’ technology, such as CDs, mobile phones, fiber optics, and satellite communications use binary numbers. We now live in a digital world, and the most important digits are 1 and 0!

Learning Objectives

After doing this activity, students should be able to:

  • Understand binary number systems and how they apply to computers and digital technology
  • Write numbers and letters in binary code
  • Decode binary numbers

Standards

National Science Education Standards

  • Content Standard A. Science as inquiry: Understanding scientific inquiry. [Grades 5 -12]
  • Content Standard E.  Science and Technology: Understanding the abilities of technological design. [Grades 5 -12]

International Technology Education Association Standards

  • H. Information and communication systems allow information to be transferred from human to human, human to machine, and machine to human. [Grades 6 – 8]
  • M. Information and communication systems allow information to be transferred from human to human, human to machine, machine to human, and machine to machine. [Grades 9 – 12]
  • The Designed World. Standard 17: Students will develop an understanding of and be able to select and use information and communications technologies.

(Note: Both the National Council of Teachers of Mathematics content standards and Common Core State Mathematics Standards emphasize counting and number systems, but not binary number operations explicitly.)

Materials

  • Your hand
  • A pen

Procedure                     

  1. Hold up one hand with fingers out-stretched.
  2. Starting from left to right, write the numbers 16, 8, 4, 2 and 1 on your fingers. If you are holding up your left hand your thumb will be number 16 and your little finger will be number one and the reverse for your right hand.
  3. We are going to use these numbers to add up to the number 26.
  4. By holding up only your little finger on your left hand you have the number 1. Holding up only your ring finger you have the number two. To get number 3 you need to hold both your little and ring finger as 1 + 2 =3. To get the number twelve you hold up your index and middle fingers and leave the others down, 8 + 4 = 12.
  5. Apologize to anyone you made a rude gesture at and tell them math is always this much fun.

How does this relate to binary numbers?                                 

  1. Looking at your hand imagine that when your fingers are curled down that fingers represent the value of zero. Standing up right your fingers represent the number one.
  2. So if all your fingers are curled down you would write your hand as 00000. If all your fingers are upright it would be 11111.
  3. Using your left hand, hold up only your little finger, curl down your thumb and the other three fingers. This is the number 1 and is written in binary code as 00001. We can see this because the first four fingers (including your thumb) are curled down and only the last finger is standing.
  4. The number 2 in binary code is 00010 because the ring finger is upright and the others are curled.
  5. How would you write the number 12? You would need the finger with the number 8 written on it and the finger with the number 4, 8 + 4 = 12. And therefore, the binary code is 01100 as the second and third fingers are upright. The number 16 is 10000.

Try your hand at coding and decoding

Binary 3

Binary 3 = 00011

We can code the alphabet by representing letters with numbers. The letter ‘a’ is the number 1, ‘b’ is 2, c = 3, d = 4 and so on until z = 26. This way you can write words as numbers. The word BINARY would be written as 2-9-14-1-18-25.

These numbers can then be coded further using binary numbers. Holding your fingers up again you can work out that the first letter of BINARY, represented by the number 2 can be written as 00010. The second letter (the number 9) is 01001.

Using this method, B-I-N-A-R-Y written in binary code is

00010 – 01001 – 01110 – 0001 – 10010 – 11001

To work out the answer to the question below, first decode the binary into decimal numbers (the numbers will be from 1 to 26) and then decode the decimal numbers in to letters.

Computer Science Unplugged offers a similar activity, “Count the Dots,” using binary number cards and worksheets with additional decoding games.

Question: What’s the difference between pea green paint and the cha cha?

Binary 12 = 01100

Binary 12 = 01100

Answer:

00001- 01110 -11001 – 01111 – 01110 – 00101

00011-00001- 01110

00011-01000- 00001 00011-01000-00001

What’s happening?

When we count and do everyday calculations like adding and multiplying, we use the decimal number system. When computers count, calculate and process words, they use the binary number system.

A visual of how to count in binary numbers from Computer Science Unplugged:

[youtube]http://www.youtube.com/watch?v=b6vHZ95XDwU[/youtube]

Using the decimal system, which is based on the number 10, the positions of the digits in a number, reading from the right, mean ‘units’, ‘tens’, ‘hundreds’, ‘thousands’, and so on. (The value of each position goes up by a factor of 10.) The decimal system uses 10 numerals (0,1,2,3,4,5,6,7,8,9) and the number 453 means 3 units, 5 tens and 4 hundreds.

Binary 16 = 10000

Binary 16 = 10000

In the binary representation of a number, the position of the digits, mean ‘units’, ‘twos’, ‘fours’, ‘eights’, ‘sixteens’, and so on. The value of each number goes up by a factor of 2. Look at your hand again, did you notice that?

The binary number system uses two numerals (0 and 1) and 1101 means (reading from the right to the left) 1 unit, no twos, 1 four and 1 eight, or 1 + 4 + 8, which equals 13. (A bi nary digi t (a 1 or a 0) is called a bit .)

The binary number system is ideal for use in computer programs because the two digits can be represented by the two states of an electronic circuit (off = 0 and on = 1).

Although computers are based on the binary number system, we don’t have to use binary numbers when using one. Instead, we enter decimal numbers the computer converts into binary before manipulating them. Fortunately, computers are much faster than we are at translating decimal into binary.

Binary codes can represent the letters of the alphabet, numerals, common symbols, and commands such as ‘space’ or ‘enter’ on the computer keyboard.

Additional Resources:

Scratch. Free programming tool developed by MIT that lets students create and share interactive stories, games, music, and art.  Includes online Scratch educators’ user community.

Computer Science Unplugged. Huge repository of free, video-rich lessons and activities designed to teach children computer science without computers.

Binary and Communication Systems hands-on activity. More fun with decoding binary numbers from lesson submitted to teachengineering.com by Tufts University’s Center for Engineering Education and Outreach.

Where can kids learn to program apps? See this TED talk by 11-year-old app developer Thomas Suarez:

[youtube]http://www.youtube.com/watch?v=na7-Bnb_Ot8[/youtube]

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