AP CSP: Number Systems Day 4: 8/30/16

Introduction : Last class we were trying to establish a way of communicating with one another by simply reading the state of a wire. We learned that the sender and receiver have to agree to a set of rules(Protocol) for any real information to be properly sent. We also learned that communicating with only two states we have to incorporate a timing system so that we can know when to stop reading the wire and when to start sending back the confirmation message. Previously you all invented ways to represent a set of messages using bits(different states). Today we’ll focus on representing many numbers using only 3 bits(states)

What is a number? How many different ways can you represent the quantity 7? Take one minute to write something down in your journal and then discuss your thoughts with the person next to you. What did you come up with?

Activity: Create your own Number Systems Today you are going to create your own number system! You will group up into 3 person groups and develop your own number systems. Given 3 places to work with, make as many unique patterns as you can using only circles, triangles and squares. Your goal is to try and create a number system anyone can use as long as they understand what the rules are for interpreting your system. How many different numbers can you represent using circles, squares, and triangles? Individual numbers can only be represented using a 3 bit pattern. See with what you can come up with your group members and record your instructions in words for interpreting. Would your system work if you could only have 2 bits to represent numbers? What about 4 or 5 bits?

Showcase your Number System Now that you’ve developed your number system, showcase it to the rest of the class. Explain the rules for your system and how many different numbers you could come up with using your system. Using your system, how do you represent the quantity 7? Were some sets of rules easier to use than others? If so what do you think led to this difference?

Discussion Were some sets of rules easier to use than others? If so what do you think led to this difference? Do you think there are any limits to the number of the symbols we could use to represent numbers? What if we only had two symbols: a circle and square? Could we still make a number system? What if we had 10 symbols: a circle, a triangle, a square, a star, and so on…Could we still make a number system?