Binary Numbers
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.
-
Mr Idosaka shows how magnetic binary number cards can be used on a whiteboard.
-
Tim demonstrates how binary numbers are stored.
-
Binary Numbers Activity at Fujitsu Kids event with JOI, Japan
-
Tim explains Binary Numbers, UOC, Christchurch, 17-18.04.2008
-
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.
-
Consider making a string of beads that code a message in binary - RAFT have a worksheet about this.
-
Sarma Singam from the University of Cincinnati has a variation on the Binary Numbers activity called Binary Encoding where students create binary numbers using positional notation with powers of 2. Students encode and decode an alphabetic message using a 6-bit encoding (Braille); the encoding is done on paper and with Candy Buttons (sugar dots on strips of paper). This activity was developed for high school students.
-
Try Engineering has an activity called 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 .
-
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.
-
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 -
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. They 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
-
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
-
Video: how Bwana explains how his binary clock works . Bwana getting excited about the binary number system.
-
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:
-
There is a card trick 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.
-
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.
-
thumbuki author Jacob Joaquin has developed an application that called Binary Clicker that converts binary numbers from 1 to 255 into music notes. Read Rick Regan's report What a Binary Counter Looks and Feels Like.
-
Another application developed by Jacob Joaquin is the Binary Music Box which is a more musical version of the Binary Clicker .
-
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 .
-
Tsubaki is a game in Japanese developed by TATSUMI Takeo which is centered around guessing a letter using a binary expression.
-
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.
-
Merchant Taylors' School UK in it's free course on Moodle aimed at AS Computing has a section called Fundamentals of Data Representation with the following resources:
- Binary to Denary Conversion includes 2 videos of explanation and also links to a Binary To Decimal Converter
- Binary Arithmetic
- Two's Complement Numbers
- Past Paper Data Representation Questions
-
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:
- Hexadecimal to Decimal Converter
- Decimal to Hexadecimal Converter
- cse4k12.org has Octal counting worksheets which is a set of worksheets that the student can use to practice counting/converting numbers in Octal.
-
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.
-
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!)
-
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
- 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:
- Exponents and Logarithms
- Place-Value Representation in Base Ten and Base Four
- See also the Homework Exercises
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 a Lesson Plan and a Poster
-
Susan Addington has developed The Number Bracelets Game to help introduce mathematical patterns.
-
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 8x8 grids where the student can draw their own black and white images and then write the corresponding binary (and hexadecimal) values.
- Crossbin Puzzles Activity that are 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.
-
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.