Computer Science LearnITWithMrC ⛯ Year 7 Year 8 Year 9 GCSE ## What do I need to Learn?

 I need to learn how to understand decimal (base 10) I need to learn how to understand binary (base 2) I need to learn how to understand that computers use binary to represent all data and instructions. I need to learn how to understand how binary can be used to represent whole numbers.

## Knowledge Organiser  ## Lesson  1. Set your Learning Objectives to red.

2. We are going to save all of our work for this topic into this PowerPoint.

3. #### To download the PowerPoint by clicking on the image below  4. Save your PowerPoint as 'Programming 1'  ## Visualizing Base-10 The denary or decimal number system is the most common number system used today. It represents numbers in base 10. As you can see below each column represents a value 10 times bigger than the previous column.

So to write the number 3140 we do so like this:  • Click on the image below to try the number base abacus
• 1. Change the base in the top left corner to 10
2. 3. Create on the abacus and then screenshot the following mixed up base 10 numbers
• 5 - Tens, 3 Hundreds, 4 Thousands, 6 Units
• 6 Hundreds, 9 Thousands, 6 Units, 8 - Ten Thousands, 4 - Tens
• ### Extension

• 11 Hundreds, 6 Thousands, 4 Units, 2 - Ten Thousands, 4 - Tens
• 7 Hundreds, 12 Thousands, 11 Units, 4 - Ten Thousands, 6 - Tens  ## What is binary?

As we have previouslt mentioned many people think that our counting system is based on 10's because we have ten fingers, and use them to count. Computers don't have fingers - they have electrical circuits, and electrical circuits have two states - on or off. Computers, therefore, use a number system based on twos, called binary.

In many ways, they are the same. In a number system based on tens, each column heading (units, tens, hundreds, etc.) is ten times the value of the column heading to its right, and you can use one of ten values (1-9 and 0) in each position. In a number system based on twos, each column heading is two times the one to its right, and you can use one of two values in each position. Here you can see a binary number with the column headings added. After the equals sign is the number as we'd normally write it.

• Go back to the number base abacus
• 1. make sure the base in the top left corner is 2
2. Create on the abacus and then screenshot the following binary numbers. Try and write their base 10 value underneath.
• 1 - Eight, 0 Fours, 1 Two, 0 Units
• 1 - Eight, 1 Four, 1 Two, 1 Unit
• ### Extension

• 1 - Sixty Four, 0 - Thirty two, 1 - Sixteen, 1 - Eight, 0 Four, 0 Two, 1 Unit
• 1 - Sixty Four, 1 - Thirty two, 0 - Sixteen, 1 - Eight, 10 Four, 1 Two, 1 Unit  • You can click each digit to toggle it between 0 and 1. If you change the binary number so that it reads 00001010, that means that you want one 8 and one 2, so the value of 00001010 is 10. It's as simple as that!
• 128
0
64
0
32
0
16
0
8
0
4
0
2
0
1
0
= 0

• Lets see how we can make 100? Is there only one pattern of 0s and 1s that make each number? A sequence of eight bits (0s or 1s), like the one shown above, is called a byte.

1. What is the maximum number that a byte can store? Screenshot your answer
2. Create the following numbers using the adding maching, screenshot each one
• 17
• 46
• 88
• 118
• 140
• 181
• 211
• 252

### Extension

• What are the values of these binary numbers
• 00101001
• 10101010
• 01011010
• 11010101
• 01011001
• 11100101
• 11111010  #### Click on the image below and see how well you can do at Binary Tetris.  ### Summing it all up

Lets look at the learning outcomes and decide which one best describes our current level of understanding :

Tick the one you feel is closest to your level

## Learning Outcomes I need to learn how to understand decimal (base 10)

• I have a basic understanding of how I can understand decimal (base 10) with a little help from my teacher
• I can show my teacher that I can understand decimal (base 10) without their help.
• I can understand decimal (base 10) independently and I can also explain it to others and can complete any extension tasks I am given.

## My Notes: Data Representation  