**Count the Dots**

The binary number system plays a central role in how information of all kinds is stored on computers. Understanding binary can lift a lot of the mystery from computers, because at a fundamental level they’re really just machines for flipping binary digits on and off. There are several activities on binary numbers in this document, all simple enough that they can be used to teach the binary system to anyone who can count! Generally children learn the binary system very quickly using this approach, but we find that many adults are also excited when they finally understand what bits and bytes really are.

### Downloads

- Binary Numbers (English)
- Arabic Language Version
- Italian Language Version
- French language Version
- Polish Language Version
- Turkish Language Version
- Greek Language Version
- Russian Language Version
- Portugese (Brazil) Language Version
- Hungarian Language Version
- Indonesian Language Version
- Slovenian Language Translation
- Tatsumi Takeo’s Analogue-Digital Conversion Activity with Decimal-Binary Conversion Extension Activity

**Videos**

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### Related Resources

- How Gangnam Style Broke YouTube – Computerphile
- National Center for Women & Information Technology (NCWIT) has a learning package called Unplugged in a Box which has detailed lesson plan of this activity.

Download the related video at Count the Dots — Binary Numbers - Mordechai (Moti) Ben-Ari from the Weizmann Institute of Science, Israel has programmed the Binary Numbers Unplugged activity in Scratch which can be downloaded in a zip file of the complete set of activities. Please read the ReadMe.txt for documentation.
- RAFT has an activity for making a string of beads that code a message in binary at Binary Weaving Worksheet.
- Try Engineering has the following activities:
- Give Binary a Try! : which explores how binary codes work, how it is applied by computer engineers to computers and other electronic equipment including clocks. Students learn how to use the code, read binary clocks, and advanced students can build their own binary clock from a kit. Download Full Lesson Plan.
- Binary and Communication Systems: Through this activity, students are introduced to the concept of binary coding as a language and its practical applications in digital and communication systems.This project is intended to give students a deeper appreciation for communication systems and an understanding of how binary symbols are used to transmit information.
- Smart Move!: This is a simple activity to visualize a communication system. In order to do this the students encode, decode, transmit, receive and store messages. They will use a code sheet and flashlight for this process. They will also maintain a storage sheet from which they can retrieve information as and when it is required.
- Texas A&M PEER has a variation of the above activity called Mountain Messages where teams communicate using flashlights and binary code

- The Greenroom resources area using the Greenfoot software has the number representation in binary using cards exercise you can download and use in the Greenfoot environment. If you are a teacher, you can apply easily to join and use the resources there.
- Daniela Marghitu’s students have programmed this activity at the Robo Camp at Auburn University. Watch the Video: RoboCamp Spring 2010 Robotics And CSUnplugged Binary Numbers Project
- Misha Leder, a Software Engineer at Google has an activity called Binary System which can be a nice extension activity. How are the numbers stored in a computer? You can think of a binary as a set of bulbs with on and off states. We look at how many numbers can be represented with a limited set of bulbs.
- Computer Science & Engineering for K-12 (cse4k12.org) has the following activities related to binary numbers below:
- Bitmaps Activity where bitmaps are a way of encoding black and white images using binary numbers. A ‘0’ is used to represents a white square in the image and a ‘1’ is used to represent a black square. These worksheets provide a set of 8×8 grids where the student can draw their own black and white images and then write the corresponding binary (and hexadecimal) values.
- Crossbin Puzzles Activity is similar to crossword puzzles except that the clues are hexadecimal numbers, and the answers are binary numbers (‘0’s and ‘1’s) instead of words. Also, once the puzzle is complete, if you fill all the ‘1’ squares with black you will see a small picture or pattern.
- Perfect Shuffles Activity: If you want to take the top card in a deck and shuffle it down to a particular position, all you need to know is the binary representation of the position where you want the card to go. Then you perform a sequence of ‘in’ and ‘out’ perfect shuffles based on the binary number and the card will be shuffled into the desired location.
- Binary Magic Trick: A set of 6 cards for a simple magic trick where you can correctly guess the secret number chosen by a student. Understanding how the trick works requires knowledge of binary.

- Centre for Innovation in Mathematics Teaching has the following teaching package in Binary Coding developed to teach Codes and Ciphers in their Maths Curriculum: Teacher Guide, Student Guide, OHP Slides, Lesson Plans

Another Exercise that might be of interest is the Find the Braille Codes. - ib computing (requires free registration) offers a complete Moodle course Data Representation in the Computer. This unit deals with the topic of Data Representation. It covers the basics of the binary number system and how binary codes (the only code that a computer can process) can be used to represent simple numbers, characters (and therefore text) and graphics.
- Online version of the binary card activity by Jim Maynard.
- Game using binary numbers available from the GitHub site, by Aruna Sankaranarayanan.
- An older version of this activity can be downloaded in PDF format here. The content is similar to the current version, but there’s some extra technical information.
- A good place to start reading is Wikipedia: Computer Numbering Formats, Wikipedia: Binary Numbers and Wikipedia: Finger Binary. Also check Wikipedia: Most Significant Bit and Wikipedia: Logic Gate
- Ron Hale-Evans has a Wiki entry called Binary Numbers System. See also Playing Card Systems.
- The Mathmaniacs web site has a similar activity (lesson 1). It includes a Binary Piano activity which is another great aid for learning binary numbers (a modified version from the University of Canterbury is available here). Mathmaniacs also have a magic trick that can be performed with binary numbers.
- Rick Garlikov has a paper on teaching binary numbers using Socratic dialogue. This approach is very empowering for students, and the general principle can apply to many of the Unplugged activities.
- Video: 9yr Old Sister Hannah Joy Counts Binary on Her Fingers
- Video: Counting to 100 in binary on your hands
- Video: A binary birthday cake
- Video: A school-house rock style video on binary numbers
- Video: Binary numbers in 60 seconds
- Video: Boolean algebra: binary numbers
- Video: Binary number system
- protowise’s Channel has two videos on introducing the concept of Two’s Complement Numbers at Video: Two’s Complement Part 1 – An Introduction and Video: Two’s Complement Part 2.
- American Public University System’s Channel has a video on Binary Arithmetic at Video: Binary Arithmetic Add – Subtract – Multiply – Divide
- Vi Hart has a Video: Binary Hand Dance , another fun way to introduce Binary!
- Thomas M. Churm has a cool Binary Clock
- A more technical explanation of binary numbers at Howstuffworks.com
- Wikipedia: Powers of Ten is a fascinating look at exponential relationships in numbers. See interesting videos on this concept below:
- Cynthia Lanius has an activity called Power Cards. This game is a very simple demonstration of the binary search technique often used for quickly retrieving data from a database. Choose a number from 1-31. Select all the cards that contain the number by clicking on them, then click on the button for the computer to guess your number. Includes a link to a Print Version and The Trick Explained. Magic Cards presents the cards in a sequential format.
- Application – Binary Numbers from the same author. Let’s use this mathe-magic trick to demonstrate a nifty way to write numbers as binary or in Base 2. Read this excellent description from the Math Forum of how computers or calculators use binary numbers.
- CISCO Systems Inc has the Binary number game
- Rick Regan reports on The Binary Marble Adding Machine. To learn about the inner workings of this machine, you may visit woodgears workshop site on binary adding machine
- Bre Pettis has a video on a Binary Count Off and another on Couting in Binary on your Fingers.
- Intuitor has an applet on counting in Binary on your fingers. For more information, please visit How to Count to 1,023 on Your Fingers
- Math Teacher Link has a lesson Binary Information: Bits and Bytes that explains that Binary Information is the basis of how computers work. In this lesson we find out why and what Bits and bytes are and how they are used.
- Daniel Robbins has written an interesting article 5 or 31? (Your fingers as binary digits) Relearning how to count on your fingers! Counting on one’s fingers and thumb (or digits) is a convenient way to physically keep track of numbers – and most everyone can do it; at least up to 5. It seems that the way we are most used to in Canada, is to unfurl our digits, one at a time, until all are unfurled. Each digit represents one number – totaling 5.
- Hiroki Manabe at Kanagawa Vocational Training School for Persons with Disabilities has developed an animation of counting in binary on your fingers, and an interactive activity to experiment with binary numbers.
- A fun animation shows binary numbers using Alice IDE at Binary Penguins by Hiroki Manabe.
- University of Tennessee Department of Computer Science has an introductory CS module intended to teach the following concepts using binary numbers using animation. Note: This site is best viewed in Internet Explorer:
- Virginia Tech, Dept of Computer Science has a complete module on Number Systems.
- See also the following number systems:
- Decimal: The decimal numeral system (also called base ten or occasionally denary) has ten as its base. Positional decimal systems include a zero and use symbols (called digits) for the ten values (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent any number, no matter how large or how small.
- Hexadecimal : uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F (or alternatively a through f) to represent values ten to fifteen.
- Octal: The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right).
- ASCII: The American Standard Code for Information Interchange (acronym: ASCII; pronounced /ˈæski/, ASS-kee)[1] is a character-encoding scheme based on the ordering of the English alphabet. ASCII codes represent text in computers, communications equipment, and other devices that use text.

- Here is a list of number converters below:
- Other converters that might be of interest:
- Computer Science & Engineering for K-12 (cse4k12.org) offers the following great activities and resources in number systems and conversion:
- Octal Counting Worksheets is a set of worksheets that the student can use to practice counting/converting numbers in Octal.
- Octal Dots worksheet has the students take an octal number and draw that many dots. After finishing, they count the number of dots in decimal to check their answer.
- Counting in Binary worksheet where the student counts from 0 to 111111 in binary (which corresponds to 0 to 63 in decimal).
- Counting in Hexadecimal worksheet helps the student count from 0 to 63 (but in hexadecimal, so it’s really 0 to 4F).
- Counting in Octal worksheet where the student counts from 0 to 77 in octal (which corresponds to 0 to 63 in decimal).
- Number Cards are Playing-card sized cards that can be used to compare the different number systems.
- Converting from Binary to Decimal Worksheet with Instructions
- Converting from Decimal to Binary Worksheet with Instructions
- Converting from Binary to Octal Worksheet with Instructions
- Converting from Binary to Hexadecimal Worksheet with Instructions

- Cleave Books has The Number Base Calculator. This calculator is concerned only with changing numbers into different bases and no attempt is made to explain what these numbers are and how they work.
- Shodor Interactivate has a unique number converter called Number Base Clocks. This activity allows you to convert between a number in a different base and base ten. The number system we are used to working in is called base 10 because there are ten digits, 0 though 9. In a base 7 number system, there would be 7 digits 0 through 6.
- SCIENCE BUDDIES offer an activity to write a number conversion program using JavaScript at Bits, Bytes, and Bases: Write a JavaScript Binary/Decimal/Hexadecimal Converter
- Kids Online Resources offer a website for definitions of different number systems and conversions at Number System.
- R Mukundan from University of Canterbury has applets to try out Binary, Octal, and Hexadecimal Numbers.
- Applets to try out different Logic Gates are developed by Do IT in their module, Computer Logic.
- Hobart and William Smith Colleges has the xLogicCircuits Lab that explores logic circuits created out of AND, OR and NOT gates. The relationship between circuits and Boolean algebra is also covered
- .Data Representation Applet which is a small applet that shows how the same 32 bits stored in the memory of a computer can represent different things, depending on how they are interpreted.
- The Peasant Algorithm and Ancient Egyptian Multiplication are tricks for doing multiplication using only doubling. At heart they are really just multiplying binary numbers. For information on how this algorithm is related to binary numbers, please read The Math Forum‘s explanation at Russian Peasant Multiplication. See also Jo Edkins‘s explanation of Ancient Egyptian Numbers and Multiplication including an online applet to try it.
- Michael S. Schneider explains how the Ancient Egyptians (and Chinese) and modern computers multiply and divide at Video: Egyptian Maths
- CS4FN has an activity related to the French Peasant’s multiplication called the The French Peasant’s Lock and Gray Code. The solution to the lock is actually something know to Computer Scientists as Gray Code : a code used in modern digital TV. Whatever, their physical form all the variations of the lock puzzle have the same solution and are logically (and so their solutions algorithmically) identical. Solve one and you’ve solved them all (Computer Scientist’s love pulling that trick with problems!)
- LessonPlanZ has a lesson plan for teaching the Egyptian Multiplication for Grades 9-12.
- Univesity of Texas College of Education has resources for teaching elementary school chidlren about binary numbers using magic tricks. See at locations below:
- Guess the Number Magic Trick
- A related activity is The Human Counting Machine

- Jo Edkins has a collection of different ways to introduce binary numbers below:
- Introduction to Binary
- Adding in Binary
- Multiplying in Binary
- A fun illustrated Binary Counter using animated figures
- Try the Binary Card Game: Based on the binary number system, where you can guess a number from 1 to 63 by having people select cards from a set of 6.
- Binary Card Game Explained
- Binary Card Game, the computer plays against you!

- Learning MATH has a teaching resource on base 2 numbers in three parts below:
- Additional resources that might be of interest:
- Video resources related to the above session:

- Math Delights has resources for teaching different base numbers by using magic cards based on the binary, base 3, or base 10 representation of numbers. See resources at Magic-Cards (Base 10) Instructions and Base 10 Cards. See also the Mathemagic Card Trick materials at Lesson Plan and a Poster
- Susan Addington has developed The Number Bracelets Game to help introduce mathematical patterns.
- John Owen has a complete set of teaching resources with lab materials in Number Systems and Bases. Important Note: These lessons are only suited for Internet Explorer!
- Computer Organisation and Design textbook has a free companion CD with a section on The Basics of Logic Design. This resource is quite advanced in terms of depth, but some basic concepts are also explained well.
- Jill Britton has the following resources in binary numbers:
- Number Representations and Conversions in Binary: Binary numbers use the same rules as decimal numbers, that is, the value of any digit (bit) depends on its position in the whole number.Decimal and
- Binary Equivalence: Use the arrows or the slider bar to explore the relationship between decimal and binary numbers from 0 to 255.Binary / Decimal Converter Calculator: Convert numbers from one system to the other
- Decimal to Binary Conversion: Convert numbers from one system to the other
- Binary Finger Counting: If you’ve ever felt seriously limited by counting on your fingers this is the solution! Count in binary. It give a whole new meaning to the number 4.
- Binary Fun Game: The objective of the game is to match a random decimal number shown by the computer, using the 8 binary keys (1 – 128). If the numbers match, you advance to the next round, and the timer increases as you advance.
- Russian Peasant Multiplication: In many sections of Russia, the peasants employed until recently what appears to be a very strange method of multiplication. Learn the method and discover its relation to the binary numbering system.
- Binary Numbers and the South Korean Flag: What do the markings on the flag of the Republic of South Korea have to do with the binary number system? What do they have to do with the number 7?
- Binary Numbers and the Chinese Zodiac: Can you locate and identify the binary numbers in this Chinese Zodiac Paper cut ?
- The Amazing Age Predictor Cards: This game is a very simple demonstration of the binary search technique often used for quickly retrieving data from a database. Choose a number from 1-31. Select all the cards that contain the number by clicking on them, then click on the button for the computer to guess your number.
- Magic Cards is another variation of the above game where the cards are in a sequential format. Note: This version seems to run only in Internet Explorer browser!
- Nim Strategy, involves adding binary numbers. Nim is an ancient game of pick up sticks for 2 players. Whoever picks up the last stick loses.
- Nim Skulls Puzzle, based on Nim, the ancient game
- Binary Numbers and the Tower of Hanoi: The binary numbers, considered in numerical order, comprise a set of sequential moves that will allow you to solve the game of the Tower of Hanoi with the minimum number of moves, specifically.
- Making a Chinese Ring Puzzle: A Chinese ring puzzle originally has 9 rings. However, to unlock those rings, we need a lot of time. So in this web-page, a puzzle which only consists of 5 rings will be made. It is believed that once you can solve a 5-ring puzzle, you will understand the algorithm to solve the original puzzle. Download the Solution. See also Wikipedia: Baguenaudier: Édouard Lucas, the inventor of the Tower of Hanoi puzzle, was known to have come up with an elegant solution which used binary and Gray codes, in the same way that his puzzle can be solved.

- Montana State University hosts activities designed by NASA in which students learn about digital images and how satellites send information and pictures to earth using the binary system. See the website complete with activities, lesson plans and assignments at Digital Images: From Satellites to the Internet.
- themathlab has a fun game called Superheroes: Our heroes love numbers to such a great extent that they have tattooed their favourite ones onto their bellies. When working as a team, our heroes can determine any number a person secretly selects as long as it falls from 1 to 31. The game comes with explanation and also large print out cards of the superheroes for classroom use at Hero Cards.
- Steve Oualline has an interesting exercise called Numbers, where one needs to write out all possible numbers that can be derived from the bit patterns 0000 to 1111.

- Ken Bigelow has a website Digital Logic that covers most topics related to binary and digital logic.
- TATSUMI Takeo from Tokyo University of Agriculture and Technology has a Kinaesthetic Activity to Demonstrate Analogue to Digital Conversion, where students make creases in paper to represent analogue data and convert them to binary data by following some simple rules. This activity comes with an extension activity for decimal to binary conversion.
- Do It Science has a fun activity called Recording Digital Data with Magnets. The goal of this project is to determine the maximum “recording density” for storing digitised information using a grid of bar magnets. You’ll learn about how information is digitised, and how the digitised information is stored magnetically.
- The Puzzle Page hosts A Binary Crossnumber Puzzle. This puzzle consists completely of binary numbers, so all the characters needed to fill in the squares will be 0s or 1s. The crossword is a 4×4 square grid, so all numbers will be written in binary, with 4 digits; e.g., 1 will be 0001, 2 will be 0010, and 4, 0100. The NOT operation changes all 0s to 1’s and all 1s to 0s; e.g., NOT(0110) is 1001 and NOT(1010) is 0101.
- Qwerty Zimbabwe has the Binary Puzzle (Colour Contact Puzzle). Designed by van Delft, Pieter and Botermans, Jack. 1997. Denkspiele der Welt. Heinrich Hugendubel Verlag, München.
- Binary Math is a great site to help students learn binary maths and the binary number system quickly, by using clear explanations and examples. Throughout its development phase, three key characteristics were kept in mind: accuracy; brevity and; completeness.
- University of Plymouth UK hosts the following resources in the PDF booklets developed for their Engineering course by Frank Hamer, Robin Horan and Martin Lavelle. These booklets offer clear explanation and lots of exercises for classroom use!
- TEACH Engineering has the following K-12 resources of interest:
- Building a Binary Mechanical Hard Drive. Students learn about the practical uses, structure, mathematics and terminology of the binary number system. They learn how to convert a given number from the binary to the decimal number system and vice versa, and perform binary addition and subtraction as part of a class game. They use this understanding to build their own simple, mechanical “hard drive” — a box that uses binary numbers to represent words for later retrieval.

See also the RGB to Hex Conversion Activity. - Binary and Communication Systems Activity is to introduce students to the concept of binary coding as a language and its practical applications in digital and communication systems.This project is intended to give students a deeper appreciation for communication systems and an understanding of how binary symbols are used to transmit information.
- Smart Move Activity is to visualise a communication system. In order to do this the students encode, decode, transmit, receive and store messages. They will use a code sheet and flash light for this process. They will also maintain a storage sheet from which they can retrieve information as and when it is required.

- Building a Binary Mechanical Hard Drive. Students learn about the practical uses, structure, mathematics and terminology of the binary number system. They learn how to convert a given number from the binary to the decimal number system and vice versa, and perform binary addition and subtraction as part of a class game. They use this understanding to build their own simple, mechanical “hard drive” — a box that uses binary numbers to represent words for later retrieval.
- NASA Space Place for Kids has some cool resources:
- All About Circuits has the following resources including some useful worksheets in Binary Math. These can be printed without solutions for classroom exercises. Teacher copy can have the answers revealed.
See also their dedicated chapters below (table of contents on the left of pages).

- Tim Fiegenbaum, North Seattle Community College has the following videos in digital logic and circuits.

- Scratch Projects User dusseau has a fun game implemented in Scratch for guessing a binary number in 60 seconds for a score with hard and easy levels called the Binary Number Quiz.
- Jeremy Falcon has an excellent article on Learning Binary and Hexadecimal. The article also comes with Hexit, a free converter tool.
- Pete Hawkes demonstrates his Binary Glove , where each finger represents a bit value in a simple binary sequence: 1, 2, 4, 8, and 16. Pressure sensors in the ends of each finger register each bit as on or off.
- PBS Online’s Animal Einsteins: Number Crunchers offers a good explanation of the number system and bases with activities and worked out answers.
- Peter Lan at University of Sydney has the Digital System Tutorial
- Kerry Redshaw has a website with information on pioneers in the history of computing. The following articles are of interest:
- Binary – So Simple a Computer Can Do It
- What’s So Logical About Boolean Algebra?
- ASCII and HTML – How They Work Together
- Gottfried Wilhelm Leibniz: Gottfried Leibniz laid the modern foundation of the movement from decimal to binary as far back as 1666 with his ‘On the Art of Combination’, laying out a method for reducing all logic to exact statements.

- Hierosolyma Kadathian‘s page on Numeric Systems defines number systems, then provides information about binary and the hexadecimal system.
- Math Steps provides a good explanation and teacher resources on Place Values :
- Southwest Educational Development Laboratory has a fun resource for elementary students called Place Value for Elementary Students. These activities reinforce students’ understanding by using rhythm, physical action, and introspection. See also Number Sense and Mathematics Communication in Elementary School. See also Wikipedia: Positional Notation
- GK-12 at Harvard University has a useful resource in Digital Circuits and Logic Gates. Description: Detailed worksheet guiding a student through understanding what digital circuits are and then through how logic gates are used to build circuits that can accomplish real-world tasks. This worksheet is also appropriate for physics students.
- Flash & Math has Truth Table Applets. Although quite advanced they allow students to practice the notation of propositional logic and the rules for constructing simple and complex truth tables. In addition, the notion of logically equivalent is addressed.
- TES Connect UK contributor 1mightyhamster has the Bits of Binary Digits Worksheet developed for year 10 and over in the UK. Note: Teachers will need to register on TES Connect UK in order to access resources.
- nrich Maths has the following activities with notes and solutions provided:
- MUKOKU UK has a module in Binary Representation of Data that covers the following topics with resources:
See also:

- Binary, Denary & Hexadecimal
- Exercises in Base Conversion
- Fixed Point Binary and Multiplication
- Exercises in Fixed Point Binary and Multiplication
- Binary Representation – Text, Images & Sound
- Binary Representation – Podcast
- More Exercises
- Error Detection & Correction
- Exercises in Error Detection & Correction

- Duncan Fyfe Gillies has some great tutorials and resources in the following topics with solutions attached:
- University of Surrey hosts The Digital Logic Tutorial Guide with the following sections of interest here:
- BBC h2g2 site has the following resources of interest in Boolean Logic:
- doit Information Technology Course has a complete course in Information Representation with lots of online activities and explanation for beginners.
- Kamal at RawKam has the following posts on the Towers of Hanoi problem:

- Wolfram Demonstrations Project has the following demonstration activities. Note: You will need to install the Wolfram CDF Player in order to use these activities. You can either download each demonstration or use your browser to run it.
- Samuel A. Rebelsky has a tutorial in The Binary System with lots of examples and tasks that could be useful for teachers
- Exploring Binary has the following interesting sections on the Powers of 2:
- The Powers of Two: Why are they called powers of two? What is the pattern you see? How is the set described mathematically? What are the set’s components? We will answer those questions in this article.
- 1,073,741,823 Grains of Rice : In the children’s book “One Grain of Rice: A Mathematical Folktale” a girl uses her knowledge of exponential growth to trick a greedy king into turning over his stockpile of rice. Hidden in the story are mathematical concepts related to doubling: powers of two, geometric sequences, geometric series, and exponents. I will analyze the story from this perspective, and then discuss my experience reading it to first and third grade students.
- Exploring Binary Numbers With PARI/GP Calculator: PARI/GP is a sophisticated tool, with several components — yet it’s easy to install and use. I use its command shell in particular, the PARI/GP calculator, or gp for short. I will show you how to use simple gp commands to explore binary numbers.
- Powers Of Two In The Josephus Problem: This formula, you won’t be surprised to hear, has connections to the powers of two and binary numbers. I will discuss my favorite solution, one based on the powers of two.
- Elements of Binary in the NCAA Basketball Tournament: If you’re like me, you also think of powers of two, binary trees, logarithms, laws of exponents, geometric sequences, geometric series, and Bernoulli trials — in short, the elements of binary numbers, binary code, and binary logic.

- tetrakys has the following games you can organise to introduce binary and other number bases. Note: some props are required to substitute these games mentioned instead of actually buying them directly. Therefore some preparation is required to create these.
- Tetradice : is a game to learn codes with different bases, from the binary code up to hexadecimal, including the decimal system. This one is a very simple game that three-year-old children can initiate and then rising its complexity as the children’s understanding increases. We suggest the children should play the TETRADICE at least for a period of three years.
- The Mystery of the Tower : This is a game that can follow the above. After the children have understood binary code with the game of the TETRADICE this game can be presented as a challenge. It should be played singly or in small groups, but every child must manage to solve it.
- The Purse for the Tetradice : The PURSE is an element that is included in the game of the TETRADICE. This element can be introduced when the children have played with different bases and have enough experience to play with hexadecimal code. The buttons and the inner slots of the pieces will be used and the children will play with these values. On the diagram is presented a chart of the values and their bases.

- NASA’s Imagine the Universe has the Detective Digit and the Slap Happy Computer Caper activity with lesson plan that will provide students with a hands-on experience in order to investigate the binary number system.
- Melvin C. Thornton has a lesson plan called Binary Numbers which is a set of activities for base 2
- Dr. John H. Lienhard has the following interesting articles on the history of different number bases:
- howtoons illustrates counting in binary numbers using cartoons:
- WVPT has an extensive lesson plan Binary, Bits, and Bytes—Oh My! by Julia Critchfield with activities
- Jeremy Kubica‘s Computational Fairy Tales has a fairy tale story Unhappy Magic Flowers and Binary
- Centre for Innovation in Mathematics Teaching has excellent teachers’ guides in the following topics:
- NCETM’s Seconday Magazine has the following articles of interest:
- Focus on…shunting, a great article on an application of binary notation in which the challenge is to rearrange railway trucks with as few shunts as possible, provide situations in which a teacher can focus on some particular ways of acting mathematically
- Focus on…perfect shuffles: There are some magic tricks that use pretty elaborate mathematics…and…magicians can perfectly shuffle a deck of cards. Explore the link to Binary numbers in this activity
- Exploring Digital Devices: exploring base 2 numbers

- Rutgers University CS has the Octopus Counting: Watch how each tentacle represents one bit. Eight tentacles = eight powers of 2! A great way to teach students how to learn the basics of binary arithmetic.
- DJ Dates has a fun activity to create a Binary Decoder Wheel which provides students with a quick way to lookup a binary number and discover the letter that the binary number represents. In class, I provide students with three printed pieces of cardstock and each student cuts out and assembles their own Binary Decoder Wheel:

- NONAMESITE.COM has Alice in BooleanLand, a game to help teach the concept of Boolean values
- Abdullah Seddiq (MIT Blossoms) has Counting Systems with teacher’s guides and additional resources. This video aims to explain counting systems (Decimal, Binary, Hexadecimal). Students will get to know how to convert numbers between these systems. Also students will learn how to do some byte and bit level operations. They will use a Visual Basic (VB) application that changes colors through logical operation on numbers. See also The Magic Picture: Steganography in Bitmap Files
- TI-Basic Developer has a section on Binary, Hexadecimal and Octal Number System which explains these systems and their applications
- Hanan Al Arfaj (MIT Blossoms) has an extension lesson: The Mailman and the Five Packages: Data Packets and Data Transfer Speed with teacher’s guides and additional resources. This video aims to explain the process of data transfer throughout computer systems and the form the data gets transferred into. Prerequisites for this lesson include some knowledge of the concept of digital data and an understanding of file size units (Bits, Bytes, Kilobytes, etc).
- Dr. Felipe H Razo has the following visual aids for learning Binary and other number systems:
- Base-2, Binary “Ripple” counting
- Base-2, Binary “Ripple” counting – A little faster!
- Adding and Subtracting Base-2, Binary Numbers
- Multiplyimg Base-2, Binary Numbers
- Binary coded Octal – Base-8 (Base 2, read in groups of 3 bits in digital telecommunications)
- Binary coded Hexadecimal – Base-16 (Base 2, read in groups of 4 bits to describe memory contents)
- Base-2, Representing Fractions – Binary-Point-8 Scale
- Base-2, Representing Fractions – Binary-Point-8 Scale – A little faster!
- Converting analog decimal to digital binary measurement
- Intra-Bases Representation Converter – Including Fractions
- Base-5, used mostly in math classes in school
- Base-60 – Used some 3,700 years ago in a region called Babylon (today’s Irak)

- Derby at OSTRICH repository of Open Educational Resources (OERs) has a Binary Tutorial (zipped) which is a collection Flash objects that can be run using Internet Explorer browser. This includes a collection of interactive exercises in Binary and other number systems
- Neuro Productions has an online application Logic Lab which can be used to demonstrate simple logic gates including a sample Binary Counter which can also be built from scratch
- Williamson Labs has a page on Digital Logic that teaches many concepts with animation and pictures
- Anthony Liekens gives designs for building an Analog Binary clock
- Attic Academy has the Basics of Binary
- Michael Littman has a great video demonstrating Logic Gates using Toys!

- Comparing Bases Used Through History

### Curriculum Links

##### Great Principles of Computer Science [info]

- Recollection

##### ACM K12 Curriculum [info]

Expand- Level I (Grades K2) Topic 11: Understand how 0s and 1s can be used to represent information, such as digital images and numbers.

##### New Zealand Curriculum [info]

Expand- Mathematics Level 2: Position and orientation
- Find rules for the next member in a sequential pattern.
- Generalise that whole numbers can be partitioned in many ways.

- Mathematics Level 3: Patterns and relationships
- Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.
- Generalise the properties of addition and subtraction with whole numbers.

- Technology Level 3: Technological systems
- Understand that technological systems are represented by symbolic language tools and understand the role played by the black box in technological systems.