1. The language of computers Before we start you need to know an important fact. Anything to the power 0 is worth 1. You will need to remember this for later!

2. A quick skills check before we start. What is the value of each of these boxes? 2323 3232 10 3 5454 8080 9191 3 2020 = 8= 9= 1000 = 9 = 625= 1 Did you spot it. Remember anything to the power 0 is 1. = 27 = 1

3. What do the following words have in common? Binary Bimodal Biped Bilateral Bicycle Bipolar These words all begin with bi and mean two

4. In binary there are only two digits. Which two would you choose? In binary code we only have the digits 0 and 1. Can you see why these might be the most important digits to use? To create larger values you need to combine 0s and 1s. How can we write 2? To help us, lets look at how we generate large numbers in decimal. and

5. Using Columns 0 1 1 0 1 1 1 0 0 2°2 1 2 2 is 0 is 1 is 2 is 3 is 4 1 0 1 is 5 1 1 0 is 6 and so on..... To count up in binary we can start with, 0, 1 and then what? This is (1 x 2 1 ) + (0 x 2°) Remember: 2° = 1 so the first column acknowledges whether there are any 1s. This is (1 x 2 1 ) + (1 x 2°) This is (1 x 2 2 ) + (0 x 2 1 ) +(0 x 2°) This is (1 x 2 2 ) + (0 x 2 1 ) +(1 x 2°) This is (1 x 2 2 ) + (1 x 2 1 ) +(0 x 2°) It’s all about the powers of 2!

6. Look at this number in binary: 1 0 0 1 11 1 x 2 0 1 x 2 1 1 x 2 2 0 x 2 3 0 x 2 4 1 x 2 5 1240032+++++= 39

7. Calculate the value of this binary number: 1 1 0 0 10 0 x 2 0 1 x 2 1 0 x 2 2 0 x 2 3 1 x 2 4 1 x 2 5 02401632+++++= 54

8. Calculate the value of this binary number: 1 0 1 1 0 01 1 x 2 0 0 x 2 1 0 x 2 2 1 x 2 3 1 x 2 4 0 x 2 5 1008160+++++= 89 1 x 2 6 +64

9. Calculate the value of this binary number: 1 1 1 0 11 1 x 2 0 1 x 2 1 0 x 2 2 0 x 2 3 1 x 2 4 1 x 2 5 12081632++ + ++= 59

10. Convert the following binary codes into decimal numbers: 1 0 1 1 0 1 01 1 0 1 1 0 0 1 0 1 0 1 0 11 1 1 0 0 0 1 1 0 1 0 1 11 0 0 0 0 0 1 = 90= 108 = 85= 56 = 107= 65

11. Let’s try it the other way round. How would you write the following in binary code? 36 63 72 21 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 1 0 1