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.

Flipping cards

Activity description (PDF)



  • Tim demonstrates how binary numbers are stored.

Related Resources

    • 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.


Curriculum Links

Great Principles of Computer Science [info]
  • Recollection
ACM K12 Curriculum [info]
  • Level I (Grades K–2) Topic 11: Understand how 0s and 1s can be used to represent information, such as digital images and numbers.
New Zealand Curriculum [info]
  • 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.