Data Representation Flashcards
What is a natural number?
- All positive whole numbers and zero
- Can be used for counting
- N = {0,1,2,3,…}
What is an integer?
- Whole numbers
- Positive and negative including zero
- Z = {…,-2,-1,0,1,2,…}
What are rational numbers?
- A number that can be expressed as a fraction
- Can be positive or negative
- Zero is a rational number
- The symbol for rational numbers is Q
What are irrational numbers?
- Cannot be written exactly as a fraction
- They have no symbol
- Examples include π or √ 2
What are real numbers?
- All possible real world quantities
- All members of irrational, rational, integers and natural numbers are real numbers
- Given the symbol R
What are ordinal numbers?
- Integers used to describe the numerical positions of objects in relation to others
What is the decimal number base?
- Base 10
- Used by humans for counting
- Uses the ten digits 0 through 9 to represent numbers
- Often called denary
What is the binary number base?
- Base 2
- Uses only two characters for each digit, either a 1 or 0
What is the hexadecimal number base?
- Base 16
- Uses the digits 0 through 9 and A to F
Why is hexadecimal useful as a shorthand representation for binary?
- Can represent numbers using far fewer digits than binary or decimal
What is a bit?
- The fundamental unit of information
- Only takes two values, a 1 or 0
What is a byte?
- A collection of 8 bits
What is a nibble?
- A collection of 4 bits, half a byte
How many values can be represented with n bits?
- 2^n values can be represented
What are the binary prefixes for quantities of bytes?
- Kibi (Ki) = 2^10
- Mebi (Mi) = 2^20
- Gibi (Gi) = 2^30
- Tebi (Ti) = 2^40
What are the decimal prefixes for quantities of bytes?
- Kilo (K) = 10^3
- Mega (M) = 10^6
- Giga (G) = 10^9
- Tera (T) = 10^12
What is underflow?
- Occurs when very small numbers are to be represented but there are not enough bits available
What is overflow?
- Occurs when a number is too large to be represented with the available bits
What is ASCII?
- Stands for American Standard Code for Information Interchange
- Uses 7 bits to represent 128 (2^7) different characters
How did ASCII become outdated?
- With the advent of the Internet, there was a requirement for an information coding system that could represent character sets other than the Latin alphabet, such as Greek or Arabic
- ASCII did not have enough bits to represent all of these character sets
What is Unicode?
- Allows the representation of a wide variety of alphabets by computers
- Uses anywhere from 8 to 48 bits per character
- Represents a much wider range of different characters than ASCII
What is a parity bit?
- Form of error checking
- A single bit is added to transmission
- This bit is used to check for errors in the transmitted data
- The bit’s value is calculated based on the transmitted data itself
What is even parity?
- The parity bit makes the total number of 1s in the transmitted data even
What is odd parity?
- The parity bit makes the total number of 1s in the transmitted data odd
What happens if an error is detected in using parity?
- The computer asks the sender to retransmit the data
What is a disadvantage of using parity bits?
- If an even number of bits are changed during transmission, the error is not detected
What is majority voting?
- Each bit is transmitted multiple times
- When received, the most commonly occuring value is taken to be correct
What is an advantage of using majority voting over parity bits?
- It doesn’t just detect the error but also corrects the error
- There’s no need for retransmission like when using parity bits
- Can correct errors when multiple bits change
What is a disadvantage of using majority voting?
- The volume of data being transmitted is increased, increasing the time taken to transmit data
What is a checksum?
- A value is appended to the transmitted data
- This value is determined by the data itself
- Once received, the recipient removes the checksum
- A check is carried out to ensure that the checksum matches the transmitted data
- If the two do not match, the recipient cannot correct the error itself
- The recipient asks the sender to retransmit the data
What is a check digit?
- Type of checksum
- Single digit added to the transmitted data
What is an advantage of using a check digit over a checksum?
- The single digit makes it so that the number of different algorithms to calculate the check digit is reduced
What is a disadvantage of using a check digit over a checksum?
- The variety of errors that the method can detect is limited
What is the difference between analogue and digital data?
- Analogue data is continuous whereas digital data is discrete
- Analogue signals can take any values and change as frequently as required
- Digital signals must always take one of a specified range of values and can only change values at specified intervals
How is a digital signal converted into an analogue signal?
- A digital to analogue converter is used
- The device reads a bit pattern representing an analogue signal
- It then outputs an alternating, analogue, electrical current
How is an analogue signal converted into a digital signal?
- An analogue signal is outputted via (e.g) microphone
- Computers use ADCs to convert the analogue signal into a digital bit pattern
- The ADC takes a reading of an analogue signal at regular intervals and records the value in a process called sampling
What is sampling?
- Samples are taken at a specific frequency
- Given in Hertz (Hz)
- Determines the number of samples taken per second
What is a bitmapped graphic?
- Images are broken into pixels
- Each pixel is assigned a binary value
- The value assigned to a pixel determined the colour of the pixel
What is the resolution of an image?
- Expressed as a number of pixels per inch
- Or the number of pixels in an image
What is the colour depth of an image?
- The number of bits assigned to a pixel
- The number of different colours that can be represented by n pixels in 2^n
How is the storage for a bitmap image calculated?
- Number of pixels x bit depth
What is metadata?
- Data about data
- Included in the storage size
- Includes the image width and height, date creation or colour depth
What is vector graphics?
- Geometric shapes and objects are used to create images
- Properties for each geometric shape or object in the image are stored in a list
Evaluate bitmapped graphics vs vector graphics
- Vector can be scaled without losing quality, bitmapped becomes blurry/pixelated when enlarged
- Vector well suited for simple images that use shapes but not photos, bitmapped used for storing photos
- Vectors use less storage space than bitmapped
What is the sampling rate?
- The number of samples per second
- Expressed in Hertz
What is the sample resolution?
- The number of bits allocated to each sample
How is the size of a sound sample calculated?
- Duration of sample in seconds x sampling rate in Hertz x sample resolution
What is the Nyquist Theorem?
- The sampling rate must be at least twice the frequency
What is MIDI?
- Stands for Musical Instrument Digital Interface
- Used with electronic musical instruments which can be connected to computers
- Stores sound as a series of event messages
- Each event message represents an event in music
What are examples of event messages in MIDI?
- The duration of a note
- The instrument with which a note is played
- How loud a note is
What are the advantages of using MIDI?
- Allows for easy manipulation of music without loss of quality
- The instruments on which notes sound can be changed
- Duration of notes can be changed
- Smaller files than sampled audio files
What are the disadvantages of using MIDI?
- Can’t be used for storing speech
- Results in a less realistic sound than sampled recordings
What is lossy compression?
- Files are reduced in size
- Some info is lost in the process
- Quality is reduced
- No limit to amount of compression applied
What is lossless compression?
- Files are reduced in size
- No info is lost
- Quality remains the same
- Limit to amount of compression applied
What is run length encoding?
- RLE is a form of lossless compression
- Removes repeated info
- Replaces it with one occurance of the info followed by the number of occurences
What is a dictionary-based method?
- Form of lossless compression
- Dictionary containing repeated data is added to the file
- Results in a reduction of size
- The dictionary must be present in the file, increasing the size of the compressed file
What is encryption?
- The process of scrambling data so that it cannot be understood if intercepted
- This keeps it secure during transmission
What is plaintext?
- Unencrypted info
What is ciphertext?
- Encrypted info
What is a cipher?
- Type of encryption method
What is a Caesar cipher?
- Encrypts info by replacing characters
- One character is always replaced by the same character
- Easily crackable
What is a Vernam cipher?
- A one-time pad cipher
- Each key should only ever be used once and should be random
- The key should be at least as long as the plaintext
- Mathematically secure
How does the Vernam cipher work?
- Aligning characters of plaintext and the key
- Converting each character to binary
- Applying XOR operation
- Converting result back to a character
