Data Representation
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