Binary Counting Script

Title Slide

Hello this is Nick Andre your at home instructor welcoming you to another i-learning exercise. In this exercise we will learn how to count in binary. Before beginning, I would recommend watching my video on number theory.

Rules of Counting

In the video I discussed the three rules of counting.

The first rule was to create a base. Since we are learning how to count in binary, our base will consist of two symbols. To keep it simple, I decided to use zero and one. Each dial or place will consist of only these two symbols.

The second rule is all about uniqueness. To successfully count no two numbers can be identical. That is to say the symbol that represents the number two cannot be the same symbol to represent the number three. Therefore use each symbol only once. Since our base consists of two symbols, I can count from zero to one and that’s it.

The second rule placed a constrained on how often a symbol can be used within the same place. It however doesn’t prevent me from creating new places. To make counting endless the third rule states when the end of the base is reached, continue on to the next place. If there is no next place create a new place and continue.

Demonstration

Allow me to demonstrate this. In the previous slide I could only count from zero to one. To count beyond one, I simply add a new place and start over. Since my dial only has two symbols, when I roll this one, it will roll back to a zero. To avoid violating the second rule I will continue my roll on to the next place. Since there is no next place, I will have to create a new place. To make it easier on us I decided to go back and add this extra place to my previous numbers. Now that this place exists I will continue my roll by changing this zero to a one creating a unique combination of symbols to represent the next number.

000

Sometimes the best way of learning is by simply doing. Like the odometer in a car, always start with the right most dial and work your way to the left. Throughout this exercise you will be asked only to click on the right most dial. On later activities you will be ask to adjust each dial accordingly.

To begin click on the first zero under the one’s column. Notice as we moved from zero to one only the first dial rolled. That is to say zero zero one in binary would represent a one in decimal.

001