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. |

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:- Change the base in the top left corner to 10
- 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
- 11 Hundreds, 6 Thousands, 4 Units, 2 - Ten Thousands, 4 - Tens
- 7 Hundreds, 12 Thousands, 11 Units, 4 - Ten Thousands, 6 - Tens

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 **ten**s, 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 **two**s, 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.

- make sure the base in the top left corner is 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
- 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

128

0

64

0

32

0

16

0

8

0

4

0

2

0

1

0

= 0

- What is the maximum number that a byte can store? Screenshot your answer
- Create the following numbers using the adding maching, screenshot each one

- 17
- 46
- 88
- 118
- 140
- 181
- 211
- 252

- 00101001
- 10101010
- 01011010
- 11010101
- 01011001
- 11100101
- 11111010

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**