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Computer Science Paper 2 > 4.5 Fundamentals of data representation > Flashcards

4.5 Fundamentals of data representation Flashcards

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1
Q

What are natural numbers, and symbol for natural numbers

A

Whole numbers including zero. N

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2
Q

What is a set

A

a defined collection of objects

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3
Q

What are integers, and symbol for integers

A

Any positive or negative numbers. Z

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4
Q

what are Rational Numbers

A

values that can be expressed as fractions including recurring numbers

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5
Q

What are irrational numbers

A

Numbers that can’t be expressed as a fraction

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6
Q

What are real numbers, and symbol for real numbers

A

all rational and irrational numbers. Represented by symbol R

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7
Q

What are ordinal numbers

A

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

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8
Q

How many numbers can be expressed with n number of bits

A

2^n

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9
Q

what are the two ways of represting quantities of bytes

A

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

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

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10
Q

What is a bit

A

fundamental unit of information

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11
Q

What prefixes does binary represnetation take (4)

A

kibi - 2^10

mebi - 2^20

gibi - 2^30

tebi - 2^40 … bytes

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12
Q

What prefixes are used in decimal prefix (4)

A

kilo - 10^3

mega - 10^6

giga - 10^9

tera - 10^12

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13
Q

What is fixed point binary and drawbacks

A

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.

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14
Q

Difference between signed and unsigned binary

A

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

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15
Q

Describe normalisation in the context of binary and floating point numbers

(4)

A

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

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16
Q

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

A

0 and 2^n -1 respectively

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17
Q

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

A

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

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18
Q

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

A

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

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19
Q

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

A

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

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20
Q

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

A

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.

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21
Q

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

A

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

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22
Q

what is ascii and characteristics

A

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

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23
Q

Why was unicode introuduced

A

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

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24
Q

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

A

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.

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25
Q

how does majority voting detect transmission errors (3)

A

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.

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26
Q

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

A

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.

27
Q

How do check digits avoid transmission errors (4)

A

A total sum off all bytes in a transmission of data is calculated using an algorithm.

The sum is often sent with the data.

The receiving computer recalculates the checksum

compares it with the checksum received or a known, expected value.

28
Q

What does analogue and digital mean in the context of data

A

analogue data - Real world data

digital - digital data

29
Q

What does analogue and digital mean in the context of signals

A

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

whereas digital signals are discrete and usually definite binary values. (1 or 0s)

30
Q

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

A

Analogue to digital conversions:

Samples are recorded at regular intervals.

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.

31
Q

What are the principles of operation of DAC

A

Digital to analogue conversions:

binary value is converted into integer value

integer value is used to quantise heights of wave

wave is recreated to output as analogue data.

(reverse of ADC)

32
Q

What are bitmapped graphics

A

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

33
Q

What is the resolutoin of a bitmap

A

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

34
Q

What is the colour depth of a bitmap

A

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.

35
Q

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

A

Image file size is determined by the number of pixels used and the number of colour combinations available(colour depth)

Ignores meta data

36
Q

What is meta data

A

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

eg width, height, colour depth.

37
Q

What are vector graphics

A

Vector images are made up of geometric objects rather than by manipulating individual pixels

The properties of each object are stored

They are retrieved in order to mathematically redraw the shape on the screen to display it.

38
Q

What are some typical properties of objects in the context of vector graphics

A

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

39
Q

what happens when images are resized using

  1. bitmapped graphics
  2. vector graphics
A
  1. Causes pixelation
  2. no loss of quality
40
Q

Which file size is typically larger, vector or bitmap?

A

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

41
Q

What is the nyquist theorem(2)

A

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.

42
Q

What is the sampling resolution when sampling sound?

What is the effect of a higher sampling resolution

A

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

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

43
Q

What is the sampling rate

What is the effect of a greater sampling rate?

A

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.

44
Q

How do we calculate sound file size

A

= sample rate x resolution x length in seconds

45
Q

What is MIDI

A

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

46
Q

How does midi differ from typical sampling

A

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

47
Q

Advantages of MIDI: (5)

A

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.

48
Q

Describe lossy compression and its advantages and disadvantages

A

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

49
Q

Describe lossless compression and its advantages and disadvantages

A

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

50
Q

What is RLE

A

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.

51
Q

Why are sound recordings often compressed

A

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.

52
Q

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

A

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.

53
Q

What is encryption

A

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

54
Q

What is cipher and cipher text

A

Cipher text - encrypted text transformed from plaintext using an encryption algorithm.

Cipher - method of encrypting used

55
Q

Describe the basic process of encryption (3)

A

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.

56
Q

Describe the caeser cipher (3)

A

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.

57
Q

Describe the vernam cipher (3)

A

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.

58
Q

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

A

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.

59
Q

What is a brute force attack

A

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

60
Q

What is frequency analysis in context on encryption

A

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.

61
Q

What is resolution in the context of sound represenation

A

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.

62
Q

In the context of floating point what is underflow?

A

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

63
Q

What problem may occur when multiplying two floating point numbers?

A

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.

Computer Science Paper 2 (7 decks)

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