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Y10 AU – P3 – Data Units and Storage Requirements

Complete this table and copy it into the OneNote document:

⏱️ Do It Now:

Answer the following questions

(1) Define what is meant by abstraction

(2) Give an example of abstraction

(3) Explain why decomposition is an important part of building any computer program

🎯 Objectives:

(1) We will be able to define the terms bit, nibble, byte, kibibyte, mebibyte, gibibyte, tebibyte

(2) We will understand that data needs to be converted into a binary format to be processed by a computer

(3) We will be able to convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa

📖 Information Source

Computers are made from transistors (switches)

Imagine millions or even billions of tiny switches working together.

Each switch stores either:
0 (off)
1 (on)
.

Binary number system

Computers use the binary number system; consisting of only 0s and 1s
Everything a computer processes must firstly be converted into a binary format
This format is used for storing numbers, text, sound, graphics and the instructions of a program

Data units

Different units are used for data storage in computers

1 bit = a single 0 or 1
1 nibble = 4 bits (half a byte)
1 byte = 8 bits = 1 character of text
1 KiB (kibibyte) = 1024 bytes
1 MiB (mebibyte) = 1024 KiB or 1024×1024 bytes
1 GiB (gibibyte) = 1024 MiB
1 TiB (tebibyte) = 1024 GiB

A Sense of Scale

n.b.

1 bit is simply a 1 or 0
1 nibble is only 4 bits, however it can be represented by a hexadecimal character!

⌨️ Activity 1a – Possible States

We calculate the possible combinations by calculating 2 to the power of how many switches there are.

(1) Complete the table below and screenshot it into OneNote

Number of Switches (Bits)	Possible Combinations or States
1	2
2	4
3
4
5
6
7
8

⌨️ Activity 1b – Storage Calculations

We calculate t

Activity 1b – Calculate The Number of Bytes

1. How many bytes are there in:

(a) 3 KiB = bytes

(b) 2.5 MiB = bytes

(d) 12 KiB = bytes

(e) 0.5 MiB = bytes

(f) 1.5 GiB = bytes

Score: 0/3

📖 Denary and Binary

Tab 1
Tab 2
Tab 3
Tab 4

The Denary System

Denary is a base 10 number system with 10 digits 0-9

Why do you think we use 10 digits?

Numbers in the Denary System

As you can see in the image below, each place value corresponds to a specific scale
e.g. ones, tens, hundreds, thousands

Binary works in a similar way

Binary place values are ones, twos, fours, eights, sixteens…. etc….

Each is twice as big as the place value to the right!

Most Significant and Least Significant Bit

✍️🧮 Converting Between Binary and Denary

(1) Complete a set of 20 Binary and Denary Conversions: Denary ↔ Binary Practice

(2) As this is for GCSE you can’t use a calculator in the exam; however you can have some scrap paper to help work it out.

(3) Paste your results into OneNote