4.5 Fundamentals of data representation UPDATED Flashcards
What are natural numbers, and symbol for natural numbers
Whole numbers including zero. N
What are the advantages and disadvantages of floating point representation
Can Represent a Wide Range of Values
Unlike fixed-point representation, floating point can store both very large and very small numbers due to its use of an exponent.
Supports Fractional and Real Numbers
More efficient use of memory
Floating point numbers cannot always represent decimal values exactly, leading to small rounding errors.
more complex and requires additional processing power compared to fixed point
What is a set
a defined collection of objects
What are integers, and symbol for integers
Any positive or negative numbers. Z
what are Rational Numbers
values that can be expressed as fractions including recurring numbers
What are irrational numbers
Numbers that can’t be expressed as a fraction
What are real numbers, and symbol for real numbers
all rational and irrational numbers. Represented by symbol R
What are ordinal numbers
a type of number used to describe the position or order of elements in a sequence or set.
How many numbers can be expressed with n number of bits
2^n
what are the two ways of represting quantities of bytes
binary prefixes (powers of 2) eg. 2^10 bytes
decimal prefixes (powers of 10) eg. 10^2 bytes
What is a bit
fundamental unit of information
What prefixes does binary represnetation take (4)
kibi - 2^10
mebi - 2^20
gibi - 2^30
tebi - 2^40 … bytes
What prefixes are used in decimal prefix (4)
kilo - 10^3
mega - 10^6
giga - 10^9
tera - 10^12
What is fixed point binary and drawbacks
Fixed point binary number have a pre determined number of bits before and after the point.
Easier to process
But they cannot represent the range or accuracy of numbers that may be required.
Difference between signed and unsigned binary
far left bit in signed binary is used to identify if the number is positive or negative
What are the minimum and maximum values for a given number of n bits in unsigned binary
0 and 2^(n-1)
Describe normalisation in the context of binary and floating point numbers
(4)
Normalisation is the process of moving the binary point of a floating point number to:
Provide the maximum level of precision for a given number of bits
ensure there is only one representation of a number.
A positive number has a sign bit of 0 and the next digit is always 1
How do we use two’s complement to represent negative numbers
the negative of a number is represented by the bitwise complement (flipping all bits) of its positive counterpart, followed by adding 1.
How do we use two’s complement to represent postitve numbers
Represented as normal except leftmost bit is a 0 to indicate it is a positive
how can numbers with at fractional part be represented in fixed point form in binary in a given number of bits
In fixed-point representation, a specific number of bits are allocated for the integer part and a specific number for the fractional part.
The position of the binary point (or decimal point) is fixed
Describe how numbers with/out a fractional part be represented in floating point form (4)
Floating Point Form:
It consists of a sign bit, exponent, and mantissa
Sign bit: Indicates whether the number is positive or negative.
Exponent: Determines the position of the binary point (similar to scientific notation in base 10).
Mantissa: The significant digits of the number.
more flexible and allows for a wider range of numbers and precision.
What is the difference between absolute and relative errors when storing and processing data in computer systems
AbsoluteError=∣TrueValue−ApproximateValue∣
Relative error = Absolute error/ True value
What is meant by range when dealing with number systems
The set of all numbers that can be represented using a specific number system
What is meant by precision when dealing with a specific number system
Maxmimum number of significant digits that can be represented
What forms other than numbers may bit patterns be used to represent (2)
Graphics
Sound
what are the limitations/rounding errors with representing decimal numbers and why they may be inaccurate
it must be capable of being represented
by a binary fraction in the given number of bits
what is ascii and what are its characteristics
American Standard Code for Information Interchange
composed of a 7 bit character set giving 128 possible binary codes
Why was unicode introuduced
introduced to standardise the encoding of characters from all languages. Unicode can support a larger range of characters
explain how parity bits are used as a way to detect errors in transmissions (4)
Computer use either odd or even parity:
In even parity, the number of 1 bits in the data plus the parity bit is even
In odd parity, the number of 1 bits in the data plus the parity bit is odd.
When the data is transmitted, the receiver can check the parity bit to see if it matches the expected parity.
If it does not match, it indicates that an error has occurred during transmission.
how does majority voting detect transmission errors (3)
Each bit of a message is sent three times
If a bit value is flipped erroneously the recipient computer uses the majority rule
assumes the two bits that have not changed were therefore correct.
Describe how check digits avoid transmission errors
check digit is an extra digit added to the end of a numerical code to help detect errors during data entry or transmission.
It is calculated using a mathematical formula applied to the other digits in the code.
When the data is received or entered, the check digit is recalculated and compared with the original. If they do not match, an error is detected.
What are check digits? Give an Example of when they are used
A check digit is an additional digit at the end of a string of numbers designed to check for mistakes in input or transmission.
FOR EXAMPLE: books have a barcode where the first 12 digits of the barcode are the unique item number, the 13th is the check digit calculated by an algorithm based on the other 12 digits.
What are digital signals
discrete and usually definite binary values. (1 or 0s)
What is analogue data
Real world data
What is digital data
information that is stored, processed, and transmitted using a binary format
What are analogue signals
Analogue signals are continuous signals that varies in amplitude and/or frequency over time,
What is a DAC when are they used context
Digital to analogue converter : digital devices (like computers) process data in binary, but many real-world applications use analog signals (e.g., sound and video)
What is a ADC when are they used context
Analogue to digital converter : digital devices (like computers) process data in binary, but many real-world applications use analog signals (e.g., sound and video)
What are the principles of operation of a ADC (4)
Analogue to digital conversions:
Samples are recorded at regular intervals. They are recorded using sensors
Each sample is quantified to measure its wave height and translate this into an integer value.
The integer value is then converted and stored digitally as a binary value.
What are the principles of operation of DAC
Digital to analogue conversions:
binary value is converted into integer value
integer value is used to quantify heights of wave
wave is recreated to output as analogue data.
(reverse of ADC)
What are bitmapped graphics
Bitmapped graphics are images created using a grid of pixels. Each pixel is given a colour value
What is the resolutoin of a bitmap
The number of pixels that make up an image is defined by the resolution.
What is the colour depth of a bitmap
A pixel is attributed a number of n bits.
The number of combinations dictates the bit depth and therefore the number of colours that can be represented.
What determines the file size of a bitmap (ignoring meta data)
Image file size is determined by the number of pixels used and the number of colour combinations available(colour depth)
FileSize(bits)=Width×Height×ColorDepth
What is meta data and some typical examples
data about data and is stored in the same file as the image data.
eg width, height, colour depth.
What are vector graphics (3)
Vector images are made up of geometric objects rather than by manipulating individual pixels
The properties of each object are stored in lists
They are retrieved in order to mathematically redraw the shape on the screen to display it.
What are some typical properties of objects in the context of vector graphics and where are they stored
The properties of objects are stored in a vector drawing list to define them.
These include:
Object type and position on the screen.
Fill colour
Line colour and weight
Length and width of radius
what happens when images are resized using
- bitmapped graphics
- vector graphics
- Causes pixelation
- no loss of quality
Advantages of vector graphics over bitmapped graphics
Smaller file size since : bitmap graphics typically larger becuase they store data about each individual pixel
Images can be resized without any loss of quality
Advantages of bitmapped graphics over vector graphics
More detailed photos: In bitmapped graphics, data is stored about each pixel, meaning you can edit individual pixels
Bitmapped graphics are directly compatible with digital displays, as these devices operate using pixels, vectors graphics may need to be converted into bitmap
Which file size is typically larger, vector or bitmap?
bitmap graphics typically larger because they store data about each individual pixel
What is the nyquist theorem(2)
Because sound is made up of many components each at different frequencies,
samples must be twice the highest frequency in order to replicate the original sound wave
This concept is known as the Nyquist theorem.
What is the sampling resolution when sampling sound?
The number of bits (audio bit depth) used to record each measurement is known as the resolution
What is the effect of a higher sampling resolution when sampling sound
More bits used per sample enables the height of the wave to be more accurately measured but increases file size.
What is the sampling rate
What is the effect of a greater sampling rate?
The frequency or number of samples taken per second affects the level of detail in the digital representation.
The greater the frequency, the greater the accuracy and file size.
How do we calculate sound file size
= sample rate x resolution x length in seconds
What is MIDI
(Musical Instrument Digital Interface) standard creates/stores sounds as request either from an instrument or piece of software.
How does midi differ from typical sampling
Midi is a system where the full sound signal does not need to be transmitted
Instead it is sent as ‘event messages’ these include:
Channel
Note on
Pitch
Volume
Velocity
Advantages of MIDI: (5)
More compact representation
Easy to modify
Easy to change values
Easy to change instruments
The MIDI file can be directly output to control an instrument.
why images and sound files are often
compressed (2 reasons)
Compression reduces the amount of data transmitted over the network, which helps save bandwidth.
Compression allows images and sound files to take up less space on storage devices
Describe lossy compression and its advantages and disadvantages
Removes data permanently to reduce file size
The original data cannot be recovered if lossy compression is used.
Describe lossless compression and its advantages and disadvantages
Recording patterns in the data rather than the data itself, The
original data can be full recovered if lossless compression has been used.
cannot reduce file size as much as lossy compression
What is RLE
Run Length Encoding:
A basic method of compression that summaries consecutive patterns of the same data
works well with image and sound data where data could be repeated many times.
Why are sound recordings often compressed
A sound recording could have many thousands of samples taken every second
The same sound or note played for a fraction of a second could result in hundred of identical samples.
How are text files often compressed and what is the method called
Dictionary Compression:
Spots regularly occurring data and stores it separately in a dictionary.
The reference to the entry in the dictionary is stored in the main file thereby reducing the original data stored.
What is encryption
a way of making sure data cannot be understood if you don’t possess the means to decrypt it.
What is cipher and cipher text
Cipher text - encrypted text transformed from plaintext using an encryption algorithm.
Cipher - method of encrypting used
Describe the basic process of encryption (3)
Plaintext of a message sent is encrypted using a cipher algorithm and key into equivalent ciphertext.
When received, the cipher text is decrypted back to plaintext using the same or different key.
Describe the caeser cipher (3)
The caesar cipher is the most basic type of encryption and the most insecure.
The encryption process is simply shifting alphabet letters of the plaintext by a consistent amount.
The caesar cipher is the most insecure as it is easy to crack.
Describe the vernam cipher (3)
Vernam cipher is, in theory, a perfect cipher, each plain text character is encrypted using its own key,
This means that there is no way for the cipher text to be deciphered without the key.
The encryption key, also known as the one time pad, is the only cipher proven to be unbreakable.
Compare the vernam cipher with the caeser cipher (4)
Vernam : perfect security, as The one-time pad is considered unbreakable
caeser: Weak security: The Caesar cipher is easily broken by modern standards, even with basic techniques like frequency analysis
Apps
Vernam: Used in secure communications where the key can be safely distributed and securely managed.
Caeser: Historically used in ancient times
What must the key be for a vernam cipher to be unbreakable (2)
The key must be:
A truly random sequence, greater or equal in length that the the plaintext and only ever used once.
Shared with the recipient by hand, independently of the message and destroyed immediately after use.
What is a brute force attack
A brute force attack is a hacking method that uses trial and error to test every possible key/combination to crack passwords
What is frequency analysis in context on encryption
Frequency analysis is the study of the frequency of letters or groups of letters in a ciphertext.
The method is used as an aid to breaking substitution ciphers.
What is resolution in the context of sound representation
refers to the precision or detail of the digital representation of the audio signal also known as the bit depth, which is the number of bits allocated to each sample.
In the context of floating point what is underflow?
underflow occurs when a calculation produces a result that is smaller in magnitude than the smallest representable normalized number.
What problem may occur when multiplying two floating point numbers?
Overflow:
If the result of the multiplication exceeds the maximum
representable value for the floating-point format (overflow),
It will then be represented by the largest representable value which may be far off the real value.
Compare fixed-point and floating-point number representations in terms of range
fixed-point has limited range
because the number of bits available for both integer and fractional parts cannot change
floating-point has much wider range
an exponent is used to move the position of the binary point
Compare fixed-point and floating-point number representations in terms of precision
fixed:
all bits can be used for a specific range of numbers without needing to store an exponent
not suited to very large or very small numbers
floating:
floating-point has lower precision than fixed-point for numbers of the same bit length
bits are divided between the mantissa and exponent
Compare fixed-point and floating-point number representations in terms of speed of calculation.
