NUMBER REPRESENTATION - Weebly...Bitmap graphics are used to represent squares S, T and U. These can...

1.1 INFORMATION REPRESENTATION

REVISION 9608 – SECTION 1 1

NUMBER REPRESENTATION QUESTION 1 (i) Convert the following binary number into hexadecimal.

1 0 1 1 1 0 0 0

(ii) Convert the following denary number into BCD format. 9 7

(iii) Using two’s complement, show how the following denary numbers could be stored in an

8-bit register:

ANSWER 1

(i) B 8 (ii) 1 0 0 1 0 1 1 1 (iii) 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 QUESTION 2 (i) Using two’s complement, show how the following denary numbers could be stored in an

8-bit register:

(ii) Convert the two numbers into hexadecimal:

124 –77

ANSWER 2

(i) 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 1 (ii) 7 C B 3



QUESTION 3 Binary Coded Decimal (BCD) is another way of representing numbers. (i) Write the number 359 in BCD form. (ii) Describe a use of BCD number representation ANSWER 3 (i) 0 0 1 1 0 1 0 1 1 0 0 1 (ii) When denary numbers need to be electronically coded. e.g. to operate displays on a calculator where each digit is represented. Decimal fractions can be accurately represented. QUESTION 4 Here are the contents of three memory locations with addresses shown in denary.

(i) What is the binary value for address 150? (ii) What is the hexadecimal value for the contents of address 152? ANSWER 4

(i) 1 0 0 1 0 1 1 0 (ii) 9 C



SOUND QUESTION 1

How sound is represented and encoded. ANSWER 1 Vibrations that travel through the air or another medium and can be heard when they reach a person's ear. When you hear different volumes of sound all that is happening is that each sound wave varies in energy for the volume (larger energy waves, the louder the sound), or distance between sound waves which adjusts the pitch (smaller distances between waves leads to higher pitched sound). Sound is recorded for:

1 channel (mono)

2 channels (stereo)

6 channels (surround sound) A computer representation of a stereo, the volume of the song varies. Sound waves in nature are continuous (analogue). This makes them very difficult to record perfectly, as computers can only store discrete data (digital). For a computer to store sound files we need to get the continuous analogue sound waves into discrete binary values.

An analogue sound wave is picked up by a microphone and sent to an Analogue-to-Digital (ADC) converter in the form of analogue electrical signals.

The ADC converts the electrical signals into digital values which can be stored on a computer.

Sound is a continuous set of data

points formed by a wave. Computers

sample this sound at discrete points to

store a digital approximation

The discrete approximations (in red)

can be used to recreate the original

sound (grey). However, due to

limitations in the number of samples

we take we are often unable to truly

represent a sound wave, though we

can get close enough for the human

ear not to notice the difference.



QUESTION 2 Give the definition of the term:

Sampling

Sampling rate

Sampling resolution ANSWER 2

Sampling o amplitude of sound wave taken at different points in time o measurement of value of analogue signal at regular time intervals.

Sampling Rate o Number of times that the amplitudes of analogue sound wave is taken/measured. o Per unit time/per second o Higher sampling rate results in more accurate digital representation.

Sampling Resolution o Resolution is the number of distinct values available to encode. o Specified by the number of bits used to store each sample. o Sometimes referred to as bit depth o The higher the sampling resolution, the smaller the quantization error o A higher sampling resolution results in less distortion of the sound o Usually 8 bet, 16 bit, 24 bit or 32 bit.

QUESTION 3 Give one reason why 16-bit sampling is used in an audio compact disc (CD). ANSWER 3 - Bit depth/sampling resolution sufficient for good quality sound - Higher bit dept/sampling resolution would mean bigger files - … hence less music content on each CD - can represent dynamic range of about 90 dB - 90 dB is basically the maximum dynamic range of human hearing - Compromise between quality and reasonable file size QUESTION 4 Give one benefit and one drawback of using a higher sampling resolution. ANSWER 4 Benefit: - Allows for larger dynamic ranges - … as dynamic range is approximately 6 times the bit depth - More accurate representation Drawback: - Bigger files/occupies more memory/space - Longer to transmit data/download music - Greater processing power needed



QUESTION 5 Describe two typical features found in software for editing sound files. ANSWER 5

Edit start time, stop time and duration of any sound Extract/delete/save part of a clip - Frequency, amplitude, pitch alteration - Fade in/out of a clip - Mix/merge multiple sound sources/tracks - Combine different sources at various volume levels - Pan between tracks/channels - Use of filters - Playback to speakers, processor or recording medium - Conversion between different audio file formats. QUESTION 6

The following information refers to a music track being recorded on a DC:

music is sampled 44100 times per second

each sample is 16 bits

each track requires sampling for left and right speakers (i) Calculate the number of bytes required to store one second of sampled music. Show your

working. (ii) A particular track is four minutes long. Describe how you would calculate the number of

megabytes required to store this track. ANSWER 6 (i) (ii) QUESTION 7

When storing music tracks in a computer, the MP3 format is often used. This reduces file size by about 90%. Explain why the music quality is apparently retained. ANSWER 7

MP3 is a lossy compressed format

uses psycho-acoustic modelling

and perceptual music/noise shaping

certain parts of the music can be eliminated without significantly degrading the listener’s experience

removes sound that the human ear can’t hear

only keeps sounds human ear can hear better than others

discards softer sound if two sounds played



IMAGES QUESTION 1

Six computer graphics terms and seven descriptions are shown below. Draw a line to link each term to its correct description.

QUESTION 2

A black and white image is 512 pixels by 256 pixels. Calculate the file size of this image in kilobytes (KB) (1 KB = 1024 bytes). Show your working. ANSWER 2



QUESTION 3 Give a reason why it is important to estimate the file size of an image. ANSWER 3

So it is possible to estimate how many images can be stored / to decide if it can be sent as an email attachment. QUESTION 4

Bitmap graphics are used to represent squares S, T and U. These can be saved in a number of different image resolutions. (i) Give the number of bits required to store each pixel for a black and white bitmap. (ii) Identify how many bits are required to store each pixel for a 256-colour bitmap. Explain your

answer ANSWER 4 (i) 1 bit. (ii) – 8 bits are needed

– Each colour is represented by one of 256 values – values 0 to 255/0000 0000 to 1111 1111 – 256 = 28

QUESTION 5

A bitmap graphic can be saved in a number of different image resolutions. (i) How many bits are required to store each pixel for a black and white bitmap? (ii) For a 256-colour bitmap, each pixel requires a byte of memory. Explain this statement. (iii) In addition to the pixel data values and its dimensions, what other information is stored in

the bitmap file? ANSWER 5 (i) 1 bit. (ii) Each colour is represented by a number. 1 byte makes possible 256 different

numbers/colours. (iii) The header and the resolution. QUESTION 6 Here are the contents of three memory locations with addresses shown in denary:

The numbers in location 151 and 152 are the height and width (in pixels) of a bitmap graphic currently in main memory. What are the dimensions of the bitmap in denary?



ANSWER 6 Height: 205 pixels Width: 156 pixels QUESTION 7

How bitmaps image is represented and encoded. ANSWER 7

Bitmap image is represented as a collection of bits that form an image. This image consists of a matrix of individual dots (or pixels) that all have their own color.

Each color of an image is stored as a binary number. In the black-and-white image below, each pixel is either black or white. You need a binary value for each different color. As each pixel is either black or white, this image can be encoded with a value of 0 for white and 1 for black.


Pixel

File header

Image resolution

Screen resolution ANSWER 8

Pixel – the smallest possible addressable area defined by a solid color in an image. Represented as binary.

File header - A file header is a ‘signature’ placed at the beginning of a file, so the operating system and other software know what to do with the following contents.

Image resolution – How many pixels does an image contains per inch/cm? The more pixels used to produce an image the more detailed that image can be.

Screen resolution – The screen resolution tells you how many pixels your screen can display horizontally and vertically. It’s written in the form 1024 x 768.

http://www.bbc.co.uk/education/guides/zqyrq6f/revision#glossary-zpnqn39




Vector graphic

Drawing List

Object

Properties

ANSWER 9

Vector graphic - Images defined using mathematics and geometry such as points, lines, curves and shapes or polygons. Allowing for scalability. Objects and properties stored mathematically.

Drawing List – a set of commands used to define a vector image. Vectors are made up of objects and their properties.

Object – is a mathematical or geometrically defined construct such as a rectangle, line or circle.

Properties – each of these objects has properties to tell you the size, colour, position, etc.



QUESTION 10 Compare between Bitmaps and Vectors. ANSWER 10

This image illustrates the difference between bitmap and vector images. The bitmap image is composed of a fixed set of dots (pixels), while the vector image is composed of a fixed set of shapes. In the picture, scaling the bitmap reveals the pixels and scaling the vector image preserves the shapes.

Vector images scale without file size increase / decrease.

Bitmap images scale resulting in file size increase / decrease.

Vector images scale without distortion to the image.

Bitmap images distort (pixelate) when scaling.

Bitmaps are better for photo editing.

Bitmaps require less processing power to display. QUESTION 11 Typical features in bitmapped and vector graphics software. ANSWER 11

Layers - Many graphic packages support the idea of 'layers'. This is where you can place images stacked within layers on top of each other in the same file. You can manipulate each layer without affecting the pixels on another layer. For example, you could change the transparency of one layer, so the layer beneath shows through. Cropping - Part of the image is cut out or removed to leave you with just the part of the graphic required. Resizing - Images can be made either larger or smaller. Rotating - Images can be rotated by an angle either clockwise or anti-clockwise. Stretching - This makes the image either taller/shorter or wider/narrower. This usually results in a distorted image. Flipping and/or Mirror Image - This flips an image either horizontally or vertically to show a mirror image.



VIDEO QUESTION 1

Give the definition of the term Video. ANSWER 1 Video is an electronic medium for recording, copying and broadcasting of moving visual images characteristics of video streams. QUESTION 2 Give the definition of the term Frame Rate (frames/second). ANSWER 2 The number of still pictures per unit of time of video. Ranges from 6 or 8 frames per second (frames/s) for old mechanical cameras. To 120 or more frames per second for new professional cameras. QUESTION 3 Give the definition of the terms:

Interlaced encoding

Progressive encoding ANSWER 3

Interlaced video is a technique for doubling the perceived frame rate of a video display without consuming extra bandwidth. The interlaced signal contains two fields of a video frame captured at two different times.

Interlacing is the practice of displaying a single frame of video as two 'half' frames. Each frame is split into alternating lines, so that the first frame displays lines 1,3,5 and so on, while the second frame of the pair displays lines 2,4,6 and so on.

QUESTION 4 Give the definition of the term Video Compression. ANSWER 4

Uncompressed video delivers maximum quality, but with a very high data rate. A variety of methods are used to compress video streams, with the most effective ones using a Group Of Pictures (GOP) to reduce spatial and temporal redundancy. QUESTION 5

Give the definition of the terms:

Spatial Redundancy

Temporal Redundancy ANSWER 5

Spatial Redundancy: is reduced by registering differences between parts of a single frame. This task is known as intraframe compression and is closely related to image compression.

Temporal Redundancy: can be reduced by registering differences between frames. This task is known as interframe compression, including motion compensation and other techniques.



QUESTION 6 Give the definition of the term Video Formats. ANSWER 6

There are different layers of video transmission and storage, each with its own set of formats to choose from. For transmission, there is a physical connector and signal protocol. A given physical link can carry certain “display standards” which specify a particular refresh rate, display resolution and color space. Many analog and digital recording formats are in use, and digital video clips can also be stored on a computer file system as files which have their own formats. In addition to the physical format used by the data storage device or transmission medium, the stream of 1s and 0s that is sent must be in a particular digital “video encoding”, of which a number are available.



COMPRESSION TECHNIQUES QUESTION 1

Explain the difference between lossless and lossy data compression techniques. ANSWER 1

lossless designed to lose none of the original detail/lossless allows original file to be recreated exactly

lossless technique based on some form of replacement

mention of type of replacement, for example RLE, FLAC etc.

by example: e.g. 000–1111–222222–333 = 3–0, 4–1, 6–2, 3–3 etc.

maximum compression about 50%

lossy may result in loss of detail compared to original file/lossy does not allow original file to be re-created exactly

lossy techniques make decision about what parts of sound/sound file are important and discards other information

only keeps sounds human ear can process/discards sounds most people cannot hear

... then applies lossless technique, for further reduction

lossy compression can reduce to about 10%

an example of jpeg, mp3 or other correct examples of compressed formats. QUESTION 2

Bitmaps may use compression techniques to reduce the file size. Explain the difference between ‘lossless’ and ‘lossy’ techniques for achieving this compression. ANSWER 2

A bitmap may contain the same sequence of pixels (i.e. a pattern) repeated many times / may contain the same pixel in a long sequence.

A lossless technique is designed to lose none of the original detail. / Lossless allows the original file to be re-created exactly. / Lossy may result in a loss of detail.

One lossless technique is ‘run-length encoding/store the colour and the number of consecutive pixels of that colour’. JPEG and GIF file formats use RLE (i.e. a lossless technique).

Lossless techniques are founded on some form of replacement.

Lossy techniques make a decision about what parts of the image are important and then discard certain information.

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