FontysICT-sem1
Binary01: Fun with Dots
Introduction
Welcome to this interactive introduction to binary numbers! We’ll learn about binary representation through a series of engaging exercises that combine magic tricks with mathematical concepts.
Part 1: The Magic Trick
The Setup
We’ll start with a magic trick.
Take the cards with numbers (see last page). Give the 6 cards to someone and ask them to:
- Choose a number that appears on at least one card (without telling you)
- Select all cards containing that number
- Give those cards to you
You’ll look at them and magically know the chosen number immediately!
The Secret
How do you know? Take the number in the top-left corner of each selected card and add them together! The sum is the chosen number.
Think about it: How does this work? Will it always work? We’ll explore this concept in detail later.
Part 2: Warm-up Exercise
Getting Started
Let’s begin with something simple. You’ll need a set of 5 cards, as shown in the picture below:
(At the end of this file you can find a link to a printable version)
Exercise 1: Basic Combinations
- Select some cards so that the total number of dots adds up to 12.
- Did you manage? Great! Now find a combination that adds up to 13 dots.
- Then 14 dots?
- And 15 dots?
- After doing some more: 16, 17, 18, 19, do you see the pattern for adding 1?
Discussion: Do you see a pattern? Try explaining it to each other!
Exercise 2: Binary Representation
Now we’ll make it more challenging and introduce binary representation!
Below, on the right side, you’ll see numbers. Using the same method as before:
- Find which cards you need for each number
- Write it down using binary notation:
- Put a ‘1’ under the dot if the card is used
- Put a ‘0’ under the dot if the card is not used
- If you can’t make the number with the given cards, cross out the number
Examples
Binary Number Representations
. . . . . needed for number 20
. . . . . needed for number 23
. . . . . needed for number 7
. . . . . is the binary representation of number 8
. . . . . is the binary representation of number 9
. . . . . is the binary representation of number 10
Observation Exercise
Do you notice anything about the even numbers? Think about:
- What do they have in common?
- How do they differ from odd numbers?
- What pattern emerges in their binary representation?
Summary
In this exercise, we’ve:
- Explored a magic trick that uses binary principles
- Practiced combining numbers using dot cards
- Introduced binary representation
- Observed patterns in number representations
The connection between the magic trick and binary numbers will become clear as you work through these exercises. Each card represents a power of 2, and the pattern of 1s and 0s you create is actually the binary representation of the number!
Next Steps
- Try creating your own number combinations
- Experiment with different card combinations
- Think about how this relates to computer memory and data storage
- Consider how this connects to the magic trick from the beginning
Hint: The magic trick works because each card’s top-left number represents a power of 2, and any number can be uniquely represented as a sum of these powers!