Denary to Binary Numbers & Binary to Denary Chapter 4 Data Representation

Units Bit – 1 bit Nibble – 4 bits Byte – 8 bits Kilobyte – 1024 bytes or 1024x8 bits Megabyte – 1024 kilobytes Gigabyte – 1024 megabytes Terabyte – 1024 gigabytes Petabyte - a unit of information equal to one thousand million million (1015) or, strictly, 250 bytes.

What is a denary number? These numbers we use in our everyday lives are called ‘denary’ numbers, it is also referred to as “Base-10”, which uses the power of 10: 1000, 100, 10, 1.

Binary Base of 2 0 1 128 64 32 16 8 4 2 1 When given a number to convert to binary you need a sequence of 0’s and 1’s. To be able to convert deniary numbers to binary you have to firstly pick the first lowest number under the decimal number given. Then how many digits backwards are you going to use to add together to make the number. e.g. 42 First lowest number under this from the table above is 32 so this is where I will start: 101010 = this will get 42 1x32 =32 0x16=0 1x8=8 0x4=0 1x2=2 0x1=0 Add all these together will get 42.

Binary Another example 228 128 64 32 16 8 4 2 1 What combinations of the numbers before will make 228? 128 64 32 16 8 4 2 1 Answer: Binary 11100100 =228 (denary)

4-bit binary numbers 13 = 9 = 14 = 11 = 7 = 5 = 8 = 8 4 2 1 Convert the following denary numbers into 4-bit binary, also referred to as Base-2. 13 = 9 = 14 = 11 = 7 = 5 = 8 = G:\ICT\Miss Elliott\Year 10 2016-2018\Chapter 3 - Data Representation\worksheet6 – Denary to Binary

Binary to denary numbers Now convert back from binary to denary 1100 0011 8 4 2 1 x X 8 + 4 + 0 + 0 =16 8 4 2 1 x X 0 + 2 + 1 =3 What would happen if the denary number was 23? Can you write this as 4-bit binary?

Binary to denary numbers Convert the following 4-bit binary numbers into whole denary numbers: 0001 = 0 = 1111 = 1100 = 0011 = G:\ICT\Miss Elliott\Year 10 2016-2018\Chapter 3 - Data Representation\worksheet6 – Denary to Binary

8-bit binary numbers =byte 128 64 32 16 8 4 2 1 Convert the following denary numbers into 8-bit binary, also referred to as Base-2. 220 = 300 = 132 = 144 = G:\ICT\Miss Elliott\Year 10 2016-2018\Chapter 3 - Data Representation\worksheet6 – Denary to Binary

Overflow What is binary overflow? http://www.bbc.co.uk/education/guides/zjfgjxs/revision/3 Watch the video and write a summary in word of what it is.

HEX to Denary Denary 5 0 Binary 0011 0010 Hex 3 2 BASE of 16 For HEX to be worked out remember: 3 2 X x 16 1 48 + 2 = 50

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

TASK: worksheet – Binary to Hex Studentshare\ICT\Miss Elliott\Yr 10\Theory2\Chapter 3 Data representation\ Worksheet 9 EXTENSION 1 on the sheet EXTENSION 2 worksheet 10

Starter http://www.atividadeseducativas.com.br/atividades/4031_binary_game/binary_game.swf

http://britton.disted.camosun.bc.ca/binary.swf

TASK: worksheet– Binary to Hex Studentshare\ICT\Miss Elliott\Yr 10\Theory2\Chapter 3 Data representation\ Worksheet 9 EXTENSION 1 on the sheet EXTENSION 2 worksheet 10

Hex to Denary to Binary 7A FE 9F 2B EXTENSION: 8C 3D EF A9 F1 A0

Bits and Bytes G:\ICT\Miss Elliott\Year 10 2016-2018\Chapter 3 - Data Representation\worksheet 11 EXTENSION

Binary Addition 0 + 0 = 0 1 +0=1 0+1=1 1+1=10

Starter http://www.atividadeseducativas.com.br/atividades/4031_binary_game/binary_game.swf

Binary Addition – worksheet 12 G:\ICT\Miss Elliott\Year 10 2016-2018\Chapter 3 - Data Representation\worksheet 12 Extension: Convert additions to denary

Binary Addition EXTENSION: Can you convert the following Denary values to Hex? 6 10 15 22 36 98 128 160

Starter 0110 1111 1111 1111 0001 0111 1111 1111 1000 0110 11111 1110 - overflow 1111 1010 1000 1000 0101 0101 1100 0011 1000 1111 1010 0001 1110 0011 0111 1001 + + + + + +

TASK - extension TASK - extension Workbook page: 79-80

Recap - starter What is binary? 0’s and 1’s switches on and off What is HEX? Base 16 What is denary? Base 10 normal whole number What is over flow? Adds up to more than 255 Extension: http://www.bbc.co.uk/education/guides/z26rcdm/test Or type in binary quiz bitesize this link is the first link

Revision Binary - 22 HEX – 2A Denary - 15

Recap Q’s – worksheet 14 - REVISION G:\ICT\Miss Elliott\Year 10 2016-2018\Chapter 3 - Data Representation What would the denary number 199 be in binary? What would the denary number 55 be in binary? What would the denary number 222 be in binary? What would 10110010 be as a denary number? What would 00101110 be as a denary number? What would 00100101 + 01000100 be as a binary number? What is an overflow error?

Starter Recap 0+0=0 1+0=1 0+1=1 1+1=10 1+1+1=11 01010111 11101110 11101100 10011000 11111110

Shifting binary numbers

DIV MOD DIV? MOD? e.g. 7/2 DIV = 3 MOD = 1

Starter http://www.teach-ict.com/gcse_new/data_info_knowledge/data_types/quiz/ontarget_data_types.htm

ASCII – American Standard Code for Information Interchange

Activity – Worksheet 13 – ASCII Table G:\ICT\Miss Elliott\Year 10 2016-2018\Chapter 3 - Data Representation EXTENSION: Create your own ASCII message

TASK - extension TASK - extension Workbook page: 81

Complete the table up to letter y starting at r G:\ICT\Miss Elliott\Year 10 2016-2018\Chapter 3 - Data Representation\worksheet 15 – ASCII Table (2)

Starter: Worksheet 15 page 2 Uni Code Complete the uni code.

Representing Images Pixels can be used to represent images. A pixel is short for picture element and is a single point in an image.

Representing Images Images are displayed as a set of pixels which form together to make an image. Visual Display Units (VDUs / monitors) display images using pixels. A true high definition monitor will have 1920 pixels in width and 1080 pixels in height. This works out at a total of approximately 2 million pixels (2,073,600).

Higher quality Image The higher the resolution (more pixels), the better quality an image will be. This is because there are more pixels which appear smaller and can’t be seen and so the ‘blocky’ pixelated effect is not noticed by the human eye. More pixels can also be used to create the image. https://www.youtube.com/watch?v=2XWzrOzq22E

Bitmaps A bitmap is an image formed from pixels. Bitmap size The size in pixels of a bitmap is calculated by multiplying the width of the image in pixels by the height of the image in pixels: Bitmap size in pixels = Width x Height The size in pixels is often referred to as the resolution of the image.

Bitmaps G:\ICT\Miss Elliott\Year 10 2016-2018\Chapter 3 - Data Representation\Worksheet 16 – Bitmap Size Left off of e-book at colour depth next

Starter – Bitmap Images What is a Bitmap Image made up of? How many pixels is this image made up of: Remember it’s the whole grid Reduce the pixels of this image what could it be changed too? What is resolution?

Bitmap Images Bitmaps are usually the most common file type for images. Bitmap images are made up of tiny dots called pixels. Each colour of each pixel is represented in binary. The number of colours available in an image is related to the number of bits the code has? What is binary made up of? Black and white images only use two colours meaning they need 1 bit to represent each pixel, 0 for white and 1 for black. 1

Worksheet 17

Colour Depth and Resolution Colour depth is the number of bits used for each pixel. The resolution is the density of pixels in an image, how many pixels are within a certain are. It is normally measure in dots per inch (DPI) The higher the resolution the more pixels in a certain area, so the better the quality of image. Increasing the colour depth or resolution means the there are more bits in the image. This improves the quality of the image but also the file size.

Bitmap file size The formula to calculate the minimum bitmap file size is: Minimum Bitmap File Size (bits) = Width x Height x Colour Depth Or Size (b) = W x H x D

Bitmap File Size Worksheet G:\ICT\Miss Elliott\Year 10 2016-2018\Chapter 3 - Data Representation\worksheet 18

Metadata Metadata is the information stored in an image file which helps the computer recreate the image on the screen from the binary data in each pixel. Metadata usually includes the images file format, height, width, colour depth and resolution. It may contain extra info such as time, date Without metadata devises would not be able to display the image on the screen.

Bitmap Images Page 82 in your books

Storing sound Sound is sampled and stored digitally. Sound is recorded by a microphone as an analogue signal. Analogue signals are pieces of continually changing data. Analogue signals need to be converted into digital data so that computers can read and store sound files. This is done by analogue to digital converters.

Sound Sampling intervals are the gaps between each of the points where the analogue recording is sampled. Sampling frequency is how many samples you take in a second. Bit rate is the number of bits used per second. Increasing the sampling frequency means the analogue recording is sampled more often. Increasing the sample size means the digital file picks up quieter sounds.

Storing Sound Page 83 in your books

Starter – Bitmap Images What is a Bitmap Image made up of? Pixels & bits What is resolution? How many pixels within the image, quality of the image What signal is sound recorded in? what does it need to be converted into? Recorded as analogue Converted into Digital What is Sampling frequency? Numbers of samples per sound/recording

Compression Data compression is when you make file sizes smaller. Take up less storage Streaming/downloading is quicker Allows loading to be quicker Email service restrictions of file sizes

Image compression Lossy Compression (JPG) Lossless Compression (PNG) The main thing to remember is that image compression reduces the file size There are two types of compression: Lossy Compression (JPG) Lossless Compression (PNG) Please remember these!

Lossy Compression (JPG) Removes data permanently Tries to reconstruct an image without the missing data Much smaller file sizes but some loss of quality Introduce image compression and explain that JPG files are automatically compressed, but this compression is only achieved by removing some of the original image data permanently. It is surprising just how much image data you can remove without noticing any degradation of quality! The compressed image on the right has been overly compressed and shows the ‘colour banding’ effect that comes of this. This is caused because the compression algorithm used to discard data looks for shades of a similar colour and groups them all as being the same colour so you see harsh bands of 10 different blues rather than a gentle gradient of millions of shades. Noticeable faults in JPG images are known as compression artefacts. 380 KB 21 KB

Lossy Compression JPG files are automatically compressed, but this compression is only achieved by removing some of the original image data permanently. It is surprising just how much image data you can remove without noticing any degradation of quality! The compressed image on the right has been overly compressed and shows the ‘colour banding’ effect that comes of this. This is caused because the compression algorithm used to discard data looks for shades of a similar colour and groups them all as being the same colour so you see harsh bands of 10 different blues rather than a gentle gradient of millions of shades. Noticeable faults in JPG images are known as compression artefacts.

Lossless compression (PNG) Finds areas of the same colour and records them as 15 blue pixels rather than blue pixel, blue pixel, blue pixel etc. 11011010,11011010,11011010,11011010 becomes 00000100-11011010 (4 lots of – 11011010) Lossless compression works by finding patterns in bit values and records the number of times they repeat instead of recording multiple instance of the same bit value. This method retains all of the information required to reconstruct the image and is known as Run Length Encoding (RLE). It will compress an image file, but not by as much as lossy methods. Demonstrate to students that lossless compression works by finding patterns in bit values and records the number of times they repeat instead of recording multiple instance of the same bit value. This method retains all of the information required to reconstruct the image and is known as Run Length Encoding (RLE). It will compress an image file, but not by as much as lossy methods. Ask students to complete Task 5 from Worksheet 3 Images.

PROS & CONS Pros Cons e.g. file type Lossy (JPG) Reduced file size More files can be stored Take up less bandwidth Lots of softwares can read lossy files Can loose data Cant be used on text files Worse quality than original file MP3 (audio) AAC (audio) JPEG (image) Lossless (PNG) Data is removed temporarily so there is no reduction in quality Can be decompressed Can be used on text files Slight reduction in file size PNG (image) FLAC (image)

Compression Page 84 in your books Pros Cons e.g. file type Lossy (JPG) Reduced file size More files can be stored Take up less bandwidth Lots of softwares can read lossy files Can loose data Cant be used on text files Worse quality than original file MP3 (audio) AAC (audio) JPEG (image) Lossless (PNG) Data is removed temporarily so there is no reduction in quality Can be decompressed Can be used on text files Slight reduction in file size PNG (image) FLAC (image)

Starter – Complete Mixed Questions Page 85 in your books

Revision for Topic Test on Thursday Homework: PP is on Show my homework. Revision guide if you wish to take one revise pages: 66-76 Page 76 gives topic Questions

Logic Gates Logic gate takes binary information and gives an output based on the boolean operator. What is a boolean operator? Logic gates are special ciruits built into computer chips. They receive binary data, apply boolean operator and then output the binary result. Each type of logic gate is shown by different symbols. Each logic gate has its own corresponding truth table. Truth table show all of the possible inputs and outputs of 1s and 0s.

NOT gate Not gate takes a single input and gives a single output. The output is always opposite value to the input. If 1 is input, it outputs 0. If 0 is the input, 1 is the output. TRUTH TABLE Input Output Input Output 1

AND gate AND gate takes two inputs and gives a single output. If 1 and 1 is the inputs, it output 1, otherwise the output is 0. TRUTH TABLE Input A Input A Input B Output 1 Output Input B

OR gate OR gate takes two inputs and gives a single output. If 1 or more inputs are 1 then the output 1, otherwise the output is 0. TRUTH TABLE Input A Input A Input B Output 1 Output Input B

Worksheet 17 – Logic Gate G:\ICT\Miss Elliott\Year 10 2016-2018\Chapter 3 - Data Representation

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