4.5 Fundamentals of data representation UPDATED

Question 1

What are natural numbers, and symbol for natural numbers

Answer 1

Whole numbers including zero. N

Question 2

What are the advantages and disadvantages of floating point representation

Answer 2

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

Question 3

What is a set

Answer 3

a defined collection of objects

Question 4

What are integers, and symbol for integers

Answer 4

Any positive or negative numbers. Z

Question 5

what are Rational Numbers

Answer 5

values that can be expressed as fractions including recurring numbers

Question 6

What are irrational numbers

Answer 6

Numbers that can’t be expressed as a fraction

Question 7

What are real numbers, and symbol for real numbers

Answer 7

all rational and irrational numbers. Represented by symbol R

Question 8

What are ordinal numbers

Answer 8

a type of number used to describe the position or order of elements in a sequence or set.

Question 9

How many numbers can be expressed with n number of bits

Answer 9

2^n

Question 10

what are the two ways of represting quantities of bytes

Answer 10

binary prefixes (powers of 2) eg. 2^10 bytes

decimal prefixes (powers of 10) eg. 10^2 bytes

Question 11

What is a bit

Answer 11

fundamental unit of information

Question 12

What prefixes does binary represnetation take (4)

Answer 12

kibi - 2^10

mebi - 2^20

gibi - 2^30

tebi - 2^40 … bytes

Question 13

What prefixes are used in decimal prefix (4)

Answer 13

kilo - 10^3

mega - 10^6

giga - 10^9

tera - 10^12

Question 14

What is fixed point binary and drawbacks

Answer 14

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.

Question 15

Difference between signed and unsigned binary

Answer 15

far left bit in signed binary is used to identify if the number is positive or negative

Question 16

What are the minimum and maximum values for a given number of n bits in unsigned binary

Answer 16

0 and 2^(n-1)

Question 17

Describe normalisation in the context of binary and floating point numbers

(4)

Answer 17

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

Question 18

How do we use two’s complement to represent negative numbers

Answer 18

the negative of a number is represented by the bitwise complement (flipping all bits) of its positive counterpart, followed by adding 1.

Question 19

How do we use two’s complement to represent postitve numbers

Answer 19

Represented as normal except leftmost bit is a 0 to indicate it is a positive

Question 20

how can numbers with at fractional part be represented in fixed point form in binary in a given number of bits

Answer 20

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

Question 21

Describe how numbers with/out a fractional part be represented in floating point form (4)

Answer 21

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.

Question 22

What is the difference between absolute and relative errors when storing and processing data in computer systems

Answer 22

AbsoluteError=∣TrueValue−ApproximateValue∣

Relative error = Absolute error/ True value

Question 23

What is meant by range when dealing with number systems

Answer 23

The set of all numbers that can be represented using a specific number system

Question 24

What is meant by precision when dealing with a specific number system

Answer 24

Maxmimum number of significant digits that can be represented

Question 25

What forms other than numbers may bit patterns be used to represent (2)

Answer 25

Graphics Sound

Question 26

what are the limitations/rounding errors with representing decimal numbers and why they may be inaccurate

Answer 26

it must be capable of being represented by a binary fraction in the given number of bits

Question 27

what is ascii and what are its characteristics

Answer 27

American Standard Code for Information Interchange composed of a 7 bit character set giving 128 possible binary codes

Question 28

Why was unicode introuduced

Answer 28

introduced to standardise the encoding of characters from all languages. Unicode can support a larger range of characters

Question 29

explain how parity bits are used as a way to detect errors in transmissions (4)

Answer 29

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.

Question 30

how does majority voting detect transmission errors (3)

Answer 30

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.

Question 31

Describe how check digits avoid transmission errors

Answer 31

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.

Question 32

What are check digits? Give an Example of when they are used

Answer 32

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.

Question 33

What are digital signals

Answer 33

discrete and usually definite binary values. (1 or 0s)

Question 34

What is analogue data

Answer 34

Real world data

Question 35

What is digital data

Answer 35

information that is stored, processed, and transmitted using a binary format

Question 36

What are analogue signals

Answer 36

Analogue signals are continuous signals that varies in amplitude and/or frequency over time,

Question 37

What is a DAC when are they used context

Answer 37

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)

Question 38

What is a ADC when are they used context

Answer 38

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)

Question 39

What are the principles of operation of a ADC (4)

Answer 39

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.

Question 40

What are the principles of operation of DAC

Answer 40

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)

Question 41

What are bitmapped graphics

Answer 41

Bitmapped graphics are images created using a grid of pixels. Each pixel is given a colour value

Question 42

What is the resolutoin of a bitmap

Answer 42

The number of pixels that make up an image is defined by the resolution.

Question 43

What is the colour depth of a bitmap

Answer 43

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.

Question 44

What determines the file size of a bitmap (ignoring meta data)

Answer 44

Image file size is determined by the number of pixels used and the number of colour combinations available(colour depth) File Size (bits)=Width×Height×Color Depth

Question 45

What is meta data and some typical examples

Answer 45

data about data and is stored in the same file as the image data. eg width, height, colour depth.

Question 46

What are vector graphics (3)

Answer 46

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.

Question 47

What are some typical properties of objects in the context of vector graphics and where are they stored

Answer 47

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

Question 48

what happens when images are resized using 1. bitmapped graphics 2. vector graphics

Answer 48

1. Causes pixelation 2. no loss of quality

Question 49

Advantages of vector graphics over bitmapped graphics

Answer 49

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

Question 50

Advantages of bitmapped graphics over vector graphics

Answer 50

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

Question 51

Which file size is typically larger, vector or bitmap?

Answer 51

bitmap graphics typically larger because they store data about each individual pixel

Question 52

What is the nyquist theorem(2)

Answer 52

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.

Question 53

What is the sampling resolution when sampling sound?

Answer 53

The number of bits (audio bit depth) used to record each measurement is known as the resolution

Question 54

What is the effect of a higher sampling resolution when sampling sound

Answer 54

More bits used per sample enables the height of the wave to be more accurately measured but increases file size.

Question 55

What is the sampling rate What is the effect of a greater sampling rate?

Answer 55

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.

Question 56

How do we calculate sound file size

Answer 56

= sample rate x resolution x length in seconds

Question 57

What is MIDI

Answer 57

(Musical Instrument Digital Interface) standard creates/stores sounds as request either from an instrument or piece of software.

Question 58

How does midi differ from typical sampling

Answer 58

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

Question 59

Advantages of MIDI: (5)

Answer 59

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.

Question 60

why images and sound files are often compressed (2 reasons)

Answer 60

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

Question 61

Describe lossy compression and its advantages and disadvantages

Answer 61

Removes data permanently to reduce file size The original data cannot be recovered if lossy compression is used.

Question 62

Describe lossless compression and its advantages and disadvantages

Answer 62

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

Question 63

What is RLE

Answer 63

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.

Question 64

Why are sound recordings often compressed

Answer 64

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.

Question 65

How are text files often compressed and what is the method called

Answer 65

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.

Question 66

What is encryption

Answer 66

a way of making sure data cannot be understood if you don't possess the means to decrypt it.

Question 67

What is cipher and cipher text

Answer 67

Cipher text - encrypted text transformed from plaintext using an encryption algorithm. Cipher - method of encrypting used

Question 68

Describe the basic process of encryption (3)

Answer 68

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.

Question 69

Describe the caeser cipher (3)

Answer 69

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.

Question 70

Describe the vernam cipher (3)

Answer 70

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.

Question 71

Compare the vernam cipher with the caeser cipher (4)

Answer 71

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

Question 72

What must the key be for a vernam cipher to be unbreakable (2)

Answer 72

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.

Question 73

What is a brute force attack

Answer 73

A brute force attack is a hacking method that uses trial and error to test every possible key/combination to crack passwords

Question 74

What is frequency analysis in context on encryption

Answer 74

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.

Question 75

What is resolution in the context of sound representation

Answer 75

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.

Question 76

In the context of floating point what is underflow?

Answer 76

underflow occurs when a calculation produces a result that is smaller in magnitude than the smallest representable normalized number.

Question 77

What problem may occur when multiplying two floating point numbers?

Answer 77

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.

Question 78

Compare fixed-point and floating-point number representations in terms of range

Answer 78

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

Question 79

Compare fixed-point and floating-point number representations in terms of precision

Answer 79

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

Question 80

Compare fixed-point and floating-point number representations in terms of speed of calculation.