# Representing Numbers

Before we begin, let's review the decimal number system. Why does 453 represent 453? (Silly question, I know...but there is a point!)

453 = (4 x 100) + (5 x 10) + (3 x 1)

Today we are going to look out how we can use binary digits (bits) to represent numbers since computers don't use the decimal system. I will need four volunteers to come to the front of the room!

• Each person is holding a card with a certain number of dots on one side and NO dots on the other
• What do you notice about the number of dots on the cards? How many dots would the next card have if we carried on to the left?
• Let's flip some cards over so the dots aren't showing. Which cards would we have to flip over to make 6? 15? 9?
• When a card is not showing, we can represent that with a zero. When it is showing, we'll use a one. What number does the binary pattern 1011 represent? What would 13 be in binary?

Group activity (Breakout!)

• Using your cards, figure out the highest number possible you can represent
• Count from 0 to the highest number using the cards. What pattern, if any, do you notice?
• Is there more than one way to get any number?
• What happens when you put a zero on the left of a binary number? What happens when you put a zero on the right of a binary number?
• Expert challenge: Try making the numbers 1, 2, 3, and 4 in order again. Can you work out a logical and reliable method of flipping the cards to increase ANY number by 1?