7_2_10

Activity 1 - READ

We (humans) understand numbers as denary; our numbers have a base of 10. Computers understand binary; binary has a base of 2. Binary numbers can be converted to human numbers and vice versa.

This is how denary works...

When we write the number 483,297 we are looking at where those numbers are placed on the number scale. Look at the image below to see what happens.

How computers think

Let’s say we have the binary number 01001010 and we need to convert it to denary. We can do this using a table to help us. Each binary digit holds a place. Like denary is 10 to the power of..., Binary is 2 to the power of...

When we put our binary number into our table we can begin to convert the number to denary. Wherever there is a 1, we count the value that applies to the placeholder. We can only ever multiply the placeholder by 1 or 0. 0 is ignored as you can see!

01001010 = 64 + 8 + 2 = 74

Activity 2

Now try one yourself. First of all, you must remember how to draw the table that helps you convert from binary to denary.

The table has these headings:

|128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

If you go from right to left then it starts and one and the number doubles each time.

Then you need a binary number to convert. Try converting 1010.

You place the number from right to left so it would appear on the table like this:

|128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

| | | | | 1 | 0 | 1 | 0 |

The numbers 8 and 2 are switched on so we add these together which makes 10.

1010 in binary is 10 in denary.

Activity 3

This game is a great way to practice converting from binary to denary:

https://studio.code.org/projects/applab/iukLbcDnzqgoxuu810unLw

Answer these questions:

• What is the largest number that you can create with 8 binary digits?
• How do you think you would create a larger number?
• Are there any other number systems that computers use? Can you find out?

Activity:

Create a fact sheet to help you remember how to convert binary to denary.

The activity below is a good introduction to binary and how it is used to represent data. You can even use torches or pretend lanterns when you act it out. Once the students have developed a way to communicate, give them a secret word to send from one partner to another.