## Binary Code Fairy Tale

Queen Accor welcomes you today to the mythical land of Alled. Unfortunately, this is not a peaceful fairy land. In this kingdom, there are many villages, all of which are being terrorized by a group of dragons. The dragons are large, angry, and ferocious. They are wreaking havoc throughout the land. Queen Accor is finding no relief and her armies cannot fight the dragons because it is difficult to know where they are. Reports are sent by horse to the queen’s castle, but the communication is too slow. Each village communicates differently that they’ve spotted a dragon. Some send up smoke signals. Some send letters to the queen. Others count the dragons and then give detailed reports at market of the number of sightings.

Queen Accor decides to make this communication easier. Each village has been asked to signal when they see a dragon by lighting a bonfire. To begin with a village lit one bonfire when they had seen one dragon, two bonfires when they had seen two dragons and so on. However, they hit a problem when they had seen four dragons; the strict health and safety laws in Alled meant that no village was allowed to light more than three bonfires at any one time. When the first village spotted four dragons, they were puzzled. How could they send a message of four when they could only light three fires?

Develop a system using only three bonfires to signal that up to a maximum of seven dragons have been seen. In other words, using 3 fires, how can you show that only one dragon was seen? How can you show that 4 were seen? How can you show that 5, 6, or 7 were seen?

(Working in pairs the children should came up with variations of using different combinations of the lit and unlit bonfires.)

Discuss the results.

Now, if each village uses a different system to report 1, 2, 3, 4, 5, 6, or 7 dragons, then they will not be able to communicate with one another and the Queen will need to understand each and every system.

So instead, Queen Accor suggested a BINARY SYSTEM for the bonfires. A binary system is a system in which every number is expressed in only two ways - zeros and ones or on and off. Using this system, a lit bonfire represents 1 and an unlit bonfire represents 0.

Discuss binary - as compared to base 10.

Therefore three lit bonfires represented 111 in binary which equals seven in decimal. If only the middle bonfire was lit then the binary code would be 010 which would represent two dragons spotted.

You must now go on a quest to explore the kingdom of Ellad. When you visit each of the villages, you should see the bonfires. Record which bonfires are lit. Return to Queen Accor and convert the binary code into the number of dragons spotted. There are 21 villages in Ellad so be sure to visit each one!

Students return with symbols and convert the code to find how many dragons have been spotted.

If time: expand the binary code to 8 digits and discuss binary strings used by computers. Ask students to give convert various binary codes (with up to 8 digits).

Queen Accor decides to make this communication easier. Each village has been asked to signal when they see a dragon by lighting a bonfire. To begin with a village lit one bonfire when they had seen one dragon, two bonfires when they had seen two dragons and so on. However, they hit a problem when they had seen four dragons; the strict health and safety laws in Alled meant that no village was allowed to light more than three bonfires at any one time. When the first village spotted four dragons, they were puzzled. How could they send a message of four when they could only light three fires?

Develop a system using only three bonfires to signal that up to a maximum of seven dragons have been seen. In other words, using 3 fires, how can you show that only one dragon was seen? How can you show that 4 were seen? How can you show that 5, 6, or 7 were seen?

(Working in pairs the children should came up with variations of using different combinations of the lit and unlit bonfires.)

Discuss the results.

Now, if each village uses a different system to report 1, 2, 3, 4, 5, 6, or 7 dragons, then they will not be able to communicate with one another and the Queen will need to understand each and every system.

So instead, Queen Accor suggested a BINARY SYSTEM for the bonfires. A binary system is a system in which every number is expressed in only two ways - zeros and ones or on and off. Using this system, a lit bonfire represents 1 and an unlit bonfire represents 0.

Discuss binary - as compared to base 10.

Therefore three lit bonfires represented 111 in binary which equals seven in decimal. If only the middle bonfire was lit then the binary code would be 010 which would represent two dragons spotted.

You must now go on a quest to explore the kingdom of Ellad. When you visit each of the villages, you should see the bonfires. Record which bonfires are lit. Return to Queen Accor and convert the binary code into the number of dragons spotted. There are 21 villages in Ellad so be sure to visit each one!

Students return with symbols and convert the code to find how many dragons have been spotted.

If time: expand the binary code to 8 digits and discuss binary strings used by computers. Ask students to give convert various binary codes (with up to 8 digits).