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.
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.
Tom Bradley, a Computer Science Graduate from Swansea has developed an online Binary Numbers activity to go along with this Unplugged module.
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:
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.
Ron Hale-Evans has a Wiki entry called Binary Numbers System. See also Playing Card Systems .
Vi Hart has a Video: Binary Hand Dance , another fun way to introduce Binary!
Thomas M. Churm has a cool Binary Clock
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.
See also 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.
See also the following number systems:
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:
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.
See also the 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:
Jo Edkins has a collection of different ways to introduce binary numbers below:
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!
Richard Bowles has a section dedicated to Representing Numbers on a Computer
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:
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.
Learn Programming (LP) has a tutorial in Introduction to decimal, binary, hexadecimal, octal and converting between bases.
Tim Gill has a booket on Computer Number Systems that teaches number conversions with good examples.
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 4x4 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:
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 .
DocDroppers has a dedicated Wiki on Learning Binary.
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 that discusses the following and more:
For a follow up of the above topics that leads to digital electronics such as registers, flip-flops, counters etc, please check out the following sections as well:
Kerry Redshaw has a website with information on pioneers in the history of computing. The following articles are of interest:
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:
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:
CSIRO's SCIENCE BY EMAIL has an activity Coin check that describe binary code, the language of computers
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:
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.
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:
Micron has the following lesson plans to teach different uses and forms of coding information and using binary code to encode and decode written language. Teachers may choose a level based on the prior knowledge of students:
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
Math Night has a module for teaching Binary Numbers:
Centre for Innovation in Mathematics Teaching has excellent teachers' guides in the following topics:
NCETM's Seconday Magazine has the following articles of interest:
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:
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
ICT essentials has a good section on Data Representation discussing how to express numbers in binary, binary-coded decimal (BCD), octal and hexadecimal.
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!