Binary Numbers A Self-Directed Mathematics Unit

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1 Binary Numbers A Self-Directed Mathematics Unit Table of Contents and Completion Checklist Information/Activity Page Date Completed Base 10 Numbers 2 Base 2 Numbers 3 Binary Number Videos 4 Binary Number Articles 4 Binary Numbers Card Activity 5-6 Counting With Binary Numbers 7 Sending Secret Messages 8 Write an Encrypted Message with Binary Numbers 9 Counting Higher Than What s It All About? 11 Online Binary Number Games 12 Number System Conversions 13 Exploring A Pattern in Binary Numbers 14 Adding in Base 10 and Binary 15 Subtracting in Base 10 and Binary 16 Multiplying in Base 10 and Binary 17 Dividing in Base 10 and Binary 18 Binary Arithmetic Worksheet Uses of Binary Numbers 21 Other Number Systems Binary Numbers Poster 24 1

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4 Watch Binary Number Videos on YouTube Watch each of these YouTube Videos to get a better understanding of Binary Numbers. Comparing Base 2 and Base 10 Khan Academy 11 minutes Binary Numbers in 60 seconds What are binary numbers and why do our computers need them? 5 minutes This has a brief intro into why we use base 10, and then shows how binary is different. This has an intro to binary numbers, plus some computer science information. 6 minutes Read Web Articles About Binary Numbers Follow the links below to read each of the articles about binary numbers. Binary Number System from Math is Fun This article introduces binary numbers. Be sure to check out the cool animation comparing binary, decimal, and hexadecimal numbers. You don t need to understand hexadecimal numbers. Why Computers Use Binary Binary Number from Wikipedia Has lots of information about binary numbers, their history, and how they work. It also has information about adding, subtracting, multiplying, and dividing in binary. 4

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9 Binary Numbers Activity Write an Encrypted Message with Binary Numbers A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Coded messages can be written with numbers when each number is assigned to a different letter as in the table above. When binary numbers are used, the code becomes even more difficult for a person break. YOUR TASK: You must write a coded message, using binary numbers, that is at least twenty letters long. 9

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12 Online Binary Number Games Find a computer with Internet access and try both of the online binary games below. You must click on number tiles to make a binary number that matches a base ten number, or you must convert the binary number shown in the tiles into a base 10 number. Record your highest score and highest level. Highest score Highest Level You Reached You must click on number tiles to make a binary number that matches the given base 10 number. There is a time limit for each problem. If you exceed the time limit or enter the wrong answer, your game is done. Try the same many times, and record the highest round that you can reach. Highest Round You Reached 12

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14 Exploring a Pattern in Binary Numbers The following information is adapted from Computer Science Unplugged, 2002 ( An interesting property of binary numbers is what happens when a zero is put on the right hand side of the number. If we are working in base 10 (decimal), when you put a zero on the right hand side of the number, it is multiplied by 10. For example, 9 becomes 90, 30 becomes 300. But what happens when you put a 0 on the right of a binary number? Try this: (9) (?) Make up at least three other examples to test your hypothesis and list them below. What is the rule? Why do you think this happens? 14

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21 Uses of Binary Numbers Even though Base 10 numbers are the only kind of numbers that most people ever see, binary numbers are EVERYWHERE. Who and what uses binary numbers and why? What makes binary numbers useful in certain situations? Your answer must be several sentences long, and it must be in your own words. Answers that are copied from websites or other sources will not be accepted. That s plagiarism! 21

22 Other Number Systems Complete the table below. Notice when a new digit is added in each number system. Base 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Base 3 (0, 1, 2) 22 Base 4 (0, 1, 2, 3) Base 5 (0, 1, 2, 3, 4)

23 Other Number Systems (continued) Complete the conversions in each table. Base 10 Base , ,000 1,000,000 Base 10 Base , ,000 1,000,000 Base 10 Base , ,000 1,000,000 Base 10 Base , ,000 1,000,000 23

24 Binary Numbers Poster For this part of the Binary Numbers Unit, you must make a poster about binary numbers that will be displayed in the classroom or in the hallway. You teacher will assign one or more of the following binary numbers poster topics: 1. Compare and contrast Base 10 numbers and Binary (Base 2) numbers. 2. Describe where binary numbers are used and why they are useful. 3. Explain how to convert from Base 10 to Binary. Show and describe some examples. 4. Explain how to convert from Binary to Base 10. Show and describe some examples. 5. Explain how to add binary numbers. Show and describe some examples. 6. Explain how to subtract binary numbers. Show and describe some examples. 7. Explain how to multiply binary numbers. Show and describe some examples. 8. Explain how to divide binary numbers. Show and describe some examples. 9. Explain how other number systems (other bases) work. Show and describe some examples. Requirements: The poster must be on a large piece of poster board. Do NOT fold it. It must have a large, easy to read title. It must be VERY neat! Posters with sloppy, handwritten text and numbers will not be accepted. If your penmanship is poor, consider typing your information and gluing it to your poster. Taping things to your poster is not acceptable. Glue or paste must be used. EVERYTHING must be in your own words. Nothing may be copied from websites or other sources. The poster must be colorful. Failure to follow any of these requirements will result in the student having to redo the poster. 24