Data Representation

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Weaknesses of majority voting

2 out of 3 data could be changed or sent wrongly so the majority may not always be right.

MP3

A digital audio encoding format that uses lossy compression.

zip

A file format that takes an existing file or files and compresses them into a single file of a smaller size.

Bit

binary digit, either 1 or 0.

text characters

collective name for upper-case letters, lower-case letters, numbers, and symbols

hexadecimal

common way of writing down large binary numbers with a base 16 number system

101

decimal value of 5

Bit

either a 1 or 0

Lossless

every single bit of data that was originally in the file remains after the file is uncompressed.

input

information from computer user

ASCII Code

2 digit hex value used to represent a character.

Byte

A collection of 8 bits

Software

A generic term for any program that can be run on a computer

Hardware

A generic term for the physical parts of the computer, both internal and external

Pictograph

A graph that organizes and shows information using pictures

Bar graph

A graph that uses bars to organize and show information

Well Ordered Set

A group of related numbers with a defined order

Address

A location in main memory used to store data and instructions.

Address

A location in main memory used to store data or instructions.

Arithmetic operation

A mathematical process that is performed on data.

Plaintext

A message before encryption.

compression

A method of reducing file sizes, particularly in digital media such as photos, audio and video.

Bitmap

A method of representing images where a picture is divided up into a grid of pixels. Each pixel is stored as a value which represents its colour.

Twos compliment

A method of working with signed binary values

Benefits of Lossless compression

A new file can be replicated exactly without any loss of data.

Binary

A number system that contains two digits, 0 and 1. Also known as base 2.

Irrational Number

A number that cannot be represented as a fraction or ratio as the decimal form will contain infinite repeating values Symbol: Q

Cardinal Number

A number that identities the size of something

Real numbers

A number that is either rational or irrational Eg. -2, -1, 0, 1, √ 2. 2, 3

Ordinal Number

A number used to identity position to relative to other numbers

Compiler

A program that translates a high level language into machine code by translating all of the code

Assembler

A program that translates a program written in assembly language into machine code

Program counter

A register in the CPU that keeps the address of the next instruction.

Accumulator

A register in the CPU that stores data currently being used by the CPU.

Bit

A single binary digit. A bit will be either a 1 or a 0.

Denary

Base 10 number system

Hexadecimal

Base 16 number system

Hexadecimal

Base 16 number system used by humans to represent groups of four bits at a time. Uses digits 0 to F.

Binary

Base 2 number system

Binary

Base 2 numbers, using 0 and 1

Octal

Base 8 numbering system

Run Length Encoding (RLE)

Basic method of compression that summarises consecutive patterns of the same data. Records one example of the sample and how many times it consecutively repeats.

Base 2

Binary

Bit

Binary Digit

Unsigned binary

Binary that represents positive numbers only

Signed binary

Binary with a positive or negative sign

Bitrate

Bitrate can also describe the quality of an audio or video file. For example, an MP3 audio file that is compressed at 192 Kbps will have a greater dynamic range and may sound slightly more clear than the same audio file compressed at 128 Kbps.

Library programs

Code, data, and resources that can be called by other programs

Compression

The process of reducing a file's size.

Rational Number

Any number that can be expressed as a fraction or ratio of integers Symbol: R

Real Number

Any positive or negative number with or without a fractional part A real number is all possible real world quantities

Integers

Any positive or negative whole numbers Eg. -2, -1, 0, 1, 2

Integer Number

Any whole number positive or negative number including zero Symbol : Z - 2 lines on the diagonal line

Unicode

At least a 16 bit character code..

Brute force attack

Attempts to apply every possible key to decrypt ciphertext until one works.

Digital

Data that is made up of separate values. How data is stored on a computer.

Base 10

Decimal / denary

Bit depth

Depends on the number of combinations and the number of colors that can be represented. A higher bit depth gives a greater range of color and better quality of image.

Image file size

Determined by the number of pixels used and number of color combinations available. No. of pixels x color depth

Types of encryption

Caesar cipher Vernam cipher

Binary Values

Can be 1 or 0

Boolean Values

Can be either True or False

Unicode advantage

Can represent a wider range of characters than ASCII and therefore more languages

Meta Data

Data about data. The meta data on an image file will describe the colour depth and the dimensions of the image. The meta data on an audio file will describe the sample resolution and the sample rate.

Metadata

Data about the data and is stored in the same file as the image data.

Benefits of reducing data requirements

Data is sent more quickly. Less bandwidth is used as transfer limits may apply. Buffering on audio and video streams is less likely to occur. Less storage is required.

Majority voting

The same set of data is sent multiple times. The multiple copies of data is compared to find discrepancies. If there is a bit different from the other copies of the data, the majority is considered the real bit. Eg. 1 0 0 is sent. Majority is 0 so it is assumed that the correct bit is 0.

bit

The short word for a "binary digit"

Byte

The smallest addressable unit of data in a computer, usually 8 bits.

Pixel

The smallest element of an image; the dots that make up the image.

Bit

The smallest unit of data (0 or 1)

bit

The smallest unit of data in computing represented by a 1 in binary.

Denary Values

Range from 0 - 9

How encryption works

Plaintext of message sent is encrypted using a cipher algorithm and key into ciphertext. Ciphertext is decrypted back to plaintext using the same or different key.

png

Portable network graphics - a digital image format that uses lossless compression.

Why does a computer need secondary storage?

Primary = volatile Secondary = non-volatile

Utility programs

Programs that perform specific common task related to running the computer, e.g. zipping files

Application software

Programs that perform specific tasks that would need doing even if computers didn't exist, e.g. carrying out calculations

Hexadecimal Values

Range from 0 - 9 then A - F

What type of number is used for measuring?

Real numbers as the range of numbers may be positive or negative and may require a fractional part

Drawbacks of lossless compression

Reduction in file size is less than lossy compression.

Pixel

Short for picture element. The smallest element of a bitmap image. Pixels are the dots the make the image on screen.

Drawbacks of lossy compression

Quality is compromised. Cannot be used for all types of data.

Colour depth

The term used to describe the number of colours that can be stored in a bitmap image. This is usually described as the number of bits set aside for each pixel. For example 8 bit colour depth can store 256 different colours.

Instruction set

The total collection of instructions that a processor can carry out.

place value

The value of the place, or position, of a digit in a number.

Operand

This is the part of the instruction that tells the CPU what to apply the operation to.

Overflow

When the result of a process (such as adding two bytes) is too big to fit in the allocated storage space. Adding two lots of 8 bits could result in a 9 bit answer for example and this would not fit in a single 8 bit byte.

Pixelate

When a bit map image is enlarged so much that you can see the individual pixels.

Overflow

When a number is too large to be represented with the number of bits allowed

Underflow

When a number is too small to be represented with the number of bits allowed

Overflow

When the result of a numeric calculation is too large to be stored in the space reserved for that type of data.

Overflow error

When the result of an addition is too large for the number of bits the computer works with

Floating Point

Where the decimal / binary point can move within a number

Translators

Software that converts programming language instructions into machine code. There are three types - compilers, assemblers, and interpreters

Drawback of MIDI

Sounds may be less realistic because sounds are synthesised.

Register

Special fast access part of the CPU that stores data.

Fixed Point

Where the decimal / binary point is fixed within a number

strings

a single character, a word, a sentence or paragraph- text

Unicode

a standard character set with around 120,000 different characters, in many different languages, current and historic

variable

a storage location paired with an associated symbolic name

Boolean variable

a variable which has only two possible values, true or false

TB

Terabyte 10¹² = 1 000 000 000 000

Tally chart

A chart that records information in sets of five

Examples of Metadata (for an image)

- Date - Width and height of image - Color depth - Location image was taken - File size

Benefits of using hexadecimal

- Easier to read and remember - Quicker to write/type - Less chance of making an error - Easy to convert to and from binary - Used to define colors, in MAC addresses, assembly language, machine code

Reasons for transmission errors

- Electrical interference - Power surges - Synchronisation issues - Wear and tear on the cables

Weaknesses of parity bit

- If two bits are interchanged, it would not be detected. - If there are bits changed but the number of 1s is still even/odd, it would not be detected.

Why is Hexadecimal used?

- It's easier to read than binary - It takes up less space when printed - Easy to convert from Hex to Binary and vice versa

Error detection methods

- Majority voting - Parity bit - Check sum - Check digit

Checksum

- Total sum of all bytes in a transmission is calculated using an algorithm - Sum is sent with the data - Receiving computer recalculates the checksum based on the data received - It compares it with the checksum sent with the data to spot any differences

Binary consists of the numbers...

...1 and 0

Denary starts at 0 then ends at...

...9

Hexadecimal goes from 0 - 9 then...

...A-F

Hexadecimal contains...

...numbers and letters

0 + 0

0 When adding binary 0 to binary 0 the result is binary 0.

Range

0 .. 2^n - 1

Binary multiplication rules

0 x 0 = 0 0 x 1 = 0 1 x 0 = 0 1 x 1 = 1

0 + 1 or 1 + 0

1 When adding 1 to 0 in binary the result is 1.

Logic gate types (6)

1. AND 2. OR 3. NOT 4. NAND 5. NOR 6. XOR

How to represent fractional numbers?

1. Fixed point 2. Floating point

1 + 1

10 When adding 1 to 1 in binary the result is 10 (zero carry 1). 10 in binary is the same as 2 in denary.

Kilobyte

1024 Bytes

Kilobyte

1024 bytes

Kilobyte (kB)

1024 bytes

Terabyte (TB)

1024 gigabytes

Terabyte (Tb)

1024 gigbytes.

Megabyte

1024 kilobytes

Megabyte (MB)

1024 kilobytes

Megabyte (Mb)

1024 kilobytes.

Gigabyte

1024 megabytes

Gigabyte (GB)

1024 megabytes

Gigabyte (Gb)

1024 megabytes.

Kilobyte

1024 or 2^10 bytes.

1 + 1 + 1

11 Three 1s added in binary is 11 (1 carry 1). 11 in binary in the same as 3 in denary.

MAC Address

12 or 16 digit hex value that identifies a device on a network.

Hex Digit

4 Binary Digits

Nibble

4 bits or half a byte

Nibble

4 bits. A nibble is equivalent to a single hexadecimal digit. e.g. 0111 = 7, 1010 = A, 1111 = F

Byte

8 Bits

Byte

8 bits

Byte

8 bits. Can be used to represent any denary number from 0 to 255 (that's 256 different combinations!). The smallest chunk of data, a byte is used to store a single ASCII character.

Unicode

A 16 ( or 32 ) bit character set that can represent 65536 (2^16) characters

Logical operation

A comparison between two items of data.

High level language 3rd generation language.

A computer programming language that is much closer to a human language than machine code. Examples of high level languages are Python, PHP, Visual Basic and C (although there are lots more!). Requires and interpreter or a compiler to turn it into machine code.

Array

A data structure where data structure where data items are grouped together under a single identifier and are then accessed based on their position

Digital

A form of signal that is constant, either on or off.

Symbol

A pattern or image used instead of words

Natural number

A positive whole number including zero

Interpreter

A program for translating high level language by translating each line one by one as the line in the source code is carried out

MP3

A standard audio file format which uses lossy compression. Compatible with most media players. Designed by the Moving picture experts group - layer 3.

Operating systems software

A suite of programs designed to control the operations of the computer

Unicode

A system of encoding text in computing widely used on the internet.

Binary

A system of numbers using only two digits, 0 and 1, also called base-2 system.

Denary

A system of numbers using ten digits, 0 and 1-9, also called the base-10 system.

Frequency table

A table that uses numbers to record data

Scheduling

A technique to ensure that different users or different programs are able to work on the same computer system at the same time

Irrational numbers

Values that cannot be expressed exactly as a fraction Eg. Pi, √ 2

Check digit

Additional digit at the end of a string of other numbers Designed to check for mistakes in input or transmission Data multiplied with its weightings Sum of the results Total is divided by 10 Remainder is subtracted from 10 Added to end of the data

ASCII

American Standard Code for Information Interchange

ASCII

American Standard Code for Information Interchange - a 7 bit character code.

ASCII

American Standard Code for Information Interchange. A 7-bit character set used for representing English keyboard characters.

Extended ASCII

An 8-bit character set that can represent 256 characters.

Overflow

An error caused by attempting to store a number that is too large for the number of bits available.

Bitmap file

An image comprised of pixels.

Bit map

An image file format where the picture is represented as a set of dots - pixels.

Bitmap

An image made up of pixels. This type of image loses quality if its width and/or height are increased.

Vector

An image stored as mathematical instructions for how to draw it. This means its width and height can be increased without the loss of quality.

Decode

An instruction is decoded by the CPU into two parts - the operator and the operand.

Parity bit

An odd or even parity is decided beforehand (depending on the machine). A parity bit is added to the end of a byte. If odd parity, there has to be an odd number of 1s. If even parity, there had to be an even number of 1s.

Continuous

Analogue how the second hand on an analogue watch displays each second and the space in between.

Analogue to digital conversion

Analogue sound samples are recorded via an amplifier. Sample is quantised to measure its wave height. Wave height is translated into an integer value. The integer value is converted and stored digitally as binary value.

analogue

Continuous data, eg the second hand on an analogue watch displays each second and the space in between.

Analogue

Continuously changing values.

Natural numbers

Counting numbers Eg. 0, 1, 2, 3

Metadata

Data about data.

metadata

Data about data. It is a set of data that describes and gives information about other data.

Process of encryption and decryption

Performed bit by bit using an exclusive or (XOR) operation with the shared key.

Difference between the character form of decimal digits and actual decimal digits

Different data types are involved, String/Character and Integer The character form cannot be used for arithmetic functions because the type of data is a character/string.

2^n ...

Different values can be represented with n bits

Bit

Each individual digit in a binary value. The smallest unit of measurement for digital data.

Ciphertext

Encrypted text/message

Key

Explains what symbols mean

Benefits of lossy compression

File size is reduced more than lossless compression. Quicker to send, move and store. Easily usable.

Two's complement

Flipping all bits and adding one

GiB

Gibibyte 2³⁰ = 1 073 741 824

GB

Gigabyte 10⁹ = 1 000 000 000

gif

Graphics interchange format - an 8-bit digital image format which uses lossless compression. Used for short animations. and where transparency is needed on the graphic. Can also be used to store simple animated images.

Vector graphics

Graphics stored as formulae.

Comparison of storage devices (HDD, SSD, CD / DVD, Blu-ray): Fragmentation

HDD: SSD: None CD / DVD: Blu-ray:

Comparison of storage devices (HDD, SSD, CD / DVD, Blu-ray): Easily portable

HDD: External disks are available SSD: External disks are available CD / DVD: Yes Blu-ray: Yes

Comparison of storage devices (HDD, SSD, CD / DVD, Blu-ray): Reliability

HDD: Good SSD: Very good CD / DVD: Fair Blu-ray: Fair

Comparison of storage devices (HDD, SSD, CD / DVD, Blu-ray): Relative power consumption

HDD: High SSD: Low CD / DVD: High Blu-ray: High

Comparison of storage devices (HDD, SSD, CD / DVD, Blu-ray): Latency

HDD: High SSD: Low CD / DVD: Very high Blu-ray: High

Comparison of storage devices (HDD, SSD, CD / DVD, Blu-ray): Typical capacity

HDD: High 1Tb SSD: Medium 500Gb CD / DVD: Low 900Mb - 1.7Gb Blu-ray: Low - medium 25-50Gb

Comparison of storage devices (HDD, SSD, CD / DVD, Blu-ray): Relative physical size

HDD: Large SSD: Small CD / DVD: Large Blu-ray: Large

Comparison of storage devices (HDD, SSD, CD / DVD, Blu-ray): Relative cost

HDD: Medium SSD: High CD / DVD: Low Blu-ray: Low

Comparison of storage devices (HDD, SSD, CD / DVD, Blu-ray): Relative speed of access

HDD: Medium SSD: High CD / DVD: Low Blu-ray: Low

Nibble

Half a byte (4 bits)

#0000FF

Hex value for the colour blue.

#FF0000

Hex value for the colour red.

Base 16

Hexadecimal

Resource management

How an operating system manages hardware and software to optimise the performance of the computer the performance of the computer

sample rate

How many samples of data are taken per second. This is normally measured in hertz, eg an audio file usually uses samples of 44.1 kHz (44,100 audio samples per second).

Sample frequency

How many sound samples are taken per second. This is measured in hertz (Hz). The higher the sample frequency the more samples are taken per second and the more like the original sound it will be when played back.

Metadata

Information about the image data that allows the computer to recreate the image from the binary data in the file. This must contain the height and width in pixels and the colour depth in bpp (bits per pixel).

Data

Information collected about people or things

digital

Information stored as discrete values usually represented as numbers. This contrasts with analogue data which is represented by continuous data, usually in waves.

pixel

Picture element - a single dot of colour in a digital bitmap image or on a computer screen.

Operating System

Is software that communicates with the hardware and allows other programs to run. It is comprised of system software, or the fundamental files your computer needs to boot up and function

JPEG

Joint Photographic Experts Group - a digital image format which uses lossy compression.

KiB

Kibibyte 2¹⁰ = 1024

Binary Prefixes

Kilo --> 2^10 = 1024, not 100

kB

Kilobyte 10³ = 1000

Machine Code

Language in Binary / Hex that is understood by the CPU

Caesar cipher

Letters of the alphabet shifted by a consistent amount.

Encryption

Making sure data cannot be understood if user has no means (key) to decrypt it. The process of converting information or data into a code, especially to prevent unauthorized access.

MiB

Mebibyte 2²⁰ = 1 048 768

MB

Megabyte 10⁶ = 1 000 000

Two's Complement

Method for representing positive and negative integers.

MIDI

Musical Instrument Digital Interface Creates sounds as requested from an instrument or software.

What type of number is used for counting?

Natural numbers as we only need to use positive whole numbers

Lossy compression

Non-essential data is permanently removed. Tries to reconstruct image without the missing data.

Limitation of using 7 character set (ASCII with 128 characters)

Not all characters on the keyboard will be represented

Resolution

Number of pixels used to make up a bitmap image.

Denary (decimal)

Numbers expressed in base 10

Hexadecimal

Numbers expressed in base 16

Ordinal numbers

Numbers used to describe the position in which values appear Eg. 1st, 2nd, 3rd

Assembly language 2nd generation language

One step up from machine code where the individual machine code instructions are represented as simple keywords such as ADD or BRA. Requires an assembler to turn it into machine code.

Vernam cipher

One time pad The key is a truly random sequence greater or equal in length than the plaintext and only ever used once. Key is shared with the recipient by hand, independently of the message and destroyed immediately after use. Eg. atmospheric noise, radioactive decay

Examples of OS, AS, UP, and translators

Operating Systems = iOS, Linux Applications = Snapchat Utility = DeFrag , McAfee Translators = Python Compiler

Operator

Part of the instruction that tells the CPU what to do.

Lossless compression

Patterns in the data are spotted and summarised in a shorter format without permanently removing any information.

Analogue

Refers to continuously changing values of a physical quantity.

Lossless compression (MP3)

Removes the sounds in the frequency ranges that cannot be heard easily / affect the perceived playback quality. Quieter notes played at the same time as louder sounds are removed.

Nyquist Theorem

Samples must be twice the highest frequency in order to replicate the original sound wave.

svg

Scalable Vector Graphics is an XML-based vector image format for two-dimensional graphics with support for interactivity and animation.

Dictionary compression

Spots regularly occuring data and stores it separately in a dictionary. Reference to entry in the dictionary is stored in the main file. Benefit: Original data stored is reduced. Drawback: Produces additional overheads

Frequency analysis

Study of the frequency of letters or groups of letters in a ciphertext to decrypt it.

Disadvantages of using 4 bytes per character.

Takes up a lot of storage Takes longer to input

Unicode disadvantage

Takes up more storage space than ASCII

Bit rate

The ................. is the space available for each sample, measured in kilobits per second (kbits/s). 128 kbits/s is 128 kilobits of sampled sound.

Machine code 1st Generation language

The 1s and 0s that make up the instructions for a computer. This is the lowest level of programming language that all programs must be converted to in order to be executed on a computer. Computers only understand machine code.

ASCII

The American Standard Code for Information Interchange. A 7-bit character set that can represent 128 characters.

colour depth

The amount of bits available for colours in an image.

Sample resolution

The amplitude (voltage of the analogue signal at that point in time). Number of bits (audio bit depth) used to record each measurement. More bits used per sample = the height of the wave to be more accurately measured = increases file size.

Character set

The complete collection of characters that can be encoded in a particular coding system.

Colour (or bit) depth

The number of bits per pixel. The more bits, the more colours can be represented.

Colour depth

The number of bits used represent the colour of a single pixel. The higher the colour depth, the more colours that can be represented.

resolution

The fineness of detail that can be seen in an image - the higher the resolution of an image, the more detail it holds. It is measured in dots per inch (dpi).

Benefits of MIDI

The full sound signal does not need to be transmitted. Only instructions to play sound is transmitted. Up to the instrument to create the sound. Significantly reduces the amount of data transferred.

Character set

The group of characters that can be represented by a computer. These can be letters, digits, space, punctuation marks and some control characters such as "escape". Each character is represented by a numerical code that is stored as a binary integer.

How a camera captures an image

The image is break up into a grid of pixels. A light sensor measures the intensity of colour in each pixel. Each measurement is converted into binary code using an analogue-to-digital convertor. Number of pixels recorded affects number of bits used and size of file created.

Sample resolution

The number of bits used to store each sound sample in an audio file. The more bits that are used for each sample the higher the sample resolution and the more like the original sound it will be when played back.

Sample Resolution

The number of bits used to store the value of each sample. The higher the number of bits the more accurately the value is stored

Resolution

The number of dots per unit length. It affects the clarity of the image.

Resolution

The number of pixels or dots per unit, for example ppi (pixels per inch).

Sampling rate

The number of samples taken in one second. Measured in Hertz. Frequency or sample rate per second affects level of detail in digital representation. Greater frequency = greater accuracy = greater file size

Sample rate

The number of times the sound is sampled per second, measured in Hz (100 Hz is 100 samples per second).

Sample rate

The number of times the sound is sampled per second, measured in Hz. The higher the rate the more accurately the sound wave is represented.

denary

The number system most commonly used by people. It contains 10 unique digits 0 to 9. Also known as decimal or base 10.

Binary

The number system we use to represent the data stored in a digital computer. Binary is a base 2 number system and uses the digits 1 and 0.

Exponent

The number written above the line and to the right of the number that indicates the power of a number

Mantissa

The part of a floating point number which represents the significant digits of that number

Operand

The part of the instruction that tells the CPU what to apply the operation to.

Operator

The part of the instruction that tells the CPU what to do.

Sampling

The process of capturing data about the sound at intervals.

Synthesis

The process of creating the sound from an audio file.

TiB

Tibibyte 2⁴⁰ = 1 099 511 627 776

upload

To add data to a server on the internet, eg you can upload videos to social media websites.

Survey

To collect data by asking questions and recording answers

downloading

To copy a file from the internet onto your computer or device.

Record

To put something in writing, pictures, or music

Boolean means

True or False

Fixed point binary

Uses a specified number of bits where the placement of the binary point is fixed.

Dot plot

Uses dots or Xs to record each piece of data above a number line

Rational numbers

Values that can be expressed as a fraction or ratio Eg. Integers, Numbers with recurring values (0.666...)

data

Units of information. In computing there can be different data types including integers, characters, and Boolean. Data is often acted on by instructions.

Unicode

Used to standardise the encoding of characters from all languages. Apply a variable length encoding of either 16 bits or 32 bits.

Byte

a group of 4 bits

byte

a group of 8 bits

Names /symbols and corresponding powers of 2 for the binary prefixes

kibi, Ki - 2^10 mebi, Mi - 2^20 gibi, Gi - 2^30 tebi, Ti - 2^40

Names / symbols and corresponding powers of 10 for the decimal prefixes

kilo, k - 10^3 mega, M - 10^6 giga, G - 10^9 tera, T - 10^12

pixel

picture element

integer

positive or negative number

Audio file size

sample rate x resolution x length in seconds

Lossy

some bits of data from the original file are permanently compressed and can not be retrieved when the file is uncompressed

colour depth

the number of bits used to represent the colours of pixels in a particular image

binary

two digits system

output

visual information displayed or printed, audio sounds, or mechanical movement


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