Fundamentals of Data representation

Question 1

Natural numbers (N)

Answer 1

The set of positive integers and 0. They can be used as cardinal(counting) or ordinal(ordering) numbers. N = {0, 1, 2, 3, …}.

Question 2

Integers (Z)

Answer 2

The set of numbers with no fractional part. The natural numbers are a subset of the integers. {…, -3, -2, -1, 0, 1, 2, 3, …}.

Question 3

Rational numbers (Q)

Answer 3

The set of numbers that can be expressed as the ratio of two integers. The integers are a subset of the rational numbers since all integers can be expressed as a ratio with 1. Q = {0, 1/2, 0.75, 0.11111…, 300.5, -42, …}.

Question 4

Irrational numbers

Answer 4

Numbers which cannot be expressed as a ratio of two integers, and hence do not lie within the set of rational numbers. {π , √2, e, …}.

Question 5

Real numbers (R)

Answer 5

The set of numbers that can represent real world quantities and have an imaginary part of 0. Rational and irrational numbers are all members of the real numbers. R = {π , 1.5, -7, 3/4, 2, 10000000, -11.3432, …}.

Question 6

Ordinal numbers

Answer 6

Natural numbers used to describe numerical position or order of objects.

Question 7

Binary

Answer 7

A number system that only uses ones and zeros to represent numbers (a base 2 system).

Question 8

Decimal

Answer 8

A number system that only uses 10 characters (0 to 9) to represent numbers 9a base 10 system).

Question 9

Hexadecimal

Answer 9

A number system that only uses 16 characters (0 to 9 and A to F) to represent numbers (a base 16 system).

Question 10

Number base

Answer 10

The number of unique digits used by a particular number system to represent numbers.

Question 11

Bit

Answer 11

A binary digit used by computers as the fundamental unit of information.

Question 12

Byte

Answer 12

A group of 8 bites.

Question 13

Binary prefix

Answer 13

A prefix to a unit representing a power of 2. (Kibi=2^10, mebi=2^20, gibi=2^30, tebi=2^40).

Question 14

Decimal prefix

Answer 14

A prefix to a unite representing a power of 10. (Kilo=10^3, mega=10^6, giga=10^9, tera=10^12).

Question 15

Signed binary

Answer 15

A binary number system that can represent both positive and negative numbers.

Question 16

Unsigned binary

Answer 16

A binary number system that can only represent positive numbers.

Question 17

Two’s complement

Answer 17

A coding scheme used in signed binary to represent negative as well as positive numbers. A negative number is represented by flipping all its digits and adding 1 to the most significant bit.

Question 18

Exponent

Answer 18

A component of floating point form that stores the number of positions to move the decimal point.

Question 19

Fixed point form

Answer 19

A form used to represent numbers with a fractional part in any number system. Digits after the fixed point are multiplied by the base raised to a negative power.

Question 20

Mantissa

Answer 20

A component of floating point form that stores the non-zero significant digits of a number.

Question 21

Rounding errors

Answer 21

Errors inherently introduced to any calculations with fixed or floating point numbers since they cannot store numbers with infinite precisions.

Question 22

Absolute error

Answer 22

The difference between the exact correct value and rounded value.

Question 23

Relative error

Answer 23

The percentage difference between the exact correct value and rounded value.

Question 24

Normalisation

Answer 24

The process of ensuring a float point number is represented as efficiently as possible by adjusting the position of the radix point and exponent.

Question 25

Underflow

Answer 25

The misrepresentation of a numeric value because it is too small to be represented with the allocated number of digits in the mantissa and exponent.

Question 26

Overflow

Answer 26

The misrepresentation of a numeric value because it is too large to be represented with the allocated number of digits in the mantissa and exponent.

Question 27

Character code

Answer 27

A unique binary representation of a character. Not to be confused with the binary representation of a decimal digit, which is it’s numerical value in the binary system.

Question 28

ASCII

Answer 28

A character set used to represent alphanumeric characters or symbols as a set of 8 bits.

Question 29

Unicode

Answer 29

A character set that is a superset of ASCII. It is used to represent alphanumeric characters or symbols as an integer code point which is equal to the character’s ASCII code.

Question 30

Check digits

Answer 30

A method of checking codes for errors during data transmission by adding an extra digit to the end (usually calculated/processed from digits in the code itself) that checks whether the data is accurate.

Question 31

Check sums

Answer 31

A method of checking codes for errors during data transmission by calculating the sum of transmitted digits.

Question 32

Majority voting

Answer 32

A method of checking binary codes for errors during data transmission by sending each bit multiple times, in a set. The receiver takes the value with the most occurrences in a set as the value for that bit.

Question 33

Parity bits

Answer 33

A method of checking binary codes for errors during data transmission by counting the number of ones and zeros present.

Question 34

Analogue data

Answer 34

Data whose values can vary continuously and take on any value between two extremes.

Question 35

Analogue signals

Answer 35

A transmission of a set of analogue data structures, that varies with time, between computational processes.

Question 36

Digital data

Answer 36

Data whose values can vary discretely and can only take on one of a finite number of values between two extremes.

Question 37

Digital signals

Answer 37

A transmission of a set of digital data structures, that varies with time, between computational processes.

Question 38

Analogue to digital converter (ADC)

Answer 38

An integrated circuit capable of converting continuous analogue data to discrete digital data for a computer.

Question 39

Digital to analogue converter (DAC)

Answer 39

An integrated circuit capable of converting discrete digital data from a computer to continuous analogue data.

Question 40

Bitmapped graphics

Answer 40

An image composed of an array of pixels each with an allocated number of bits, arranged to form an image. Also known as raster graphics.

Question 41

Bitmap storage requirements

Answer 41

The amount of storage required for a bitmapped image is at least its
(image size) x (colour depth).

Question 42

Colour depth

Answer 42

A measure of the amount of colour used in an image, expressed in terms of the number of bits per pixel.

Question 43

Image size

Answer 43

The total number of pixels in an image expressed in terms of its dimensions:
(width in pixels) x (height in pixels).

Question 44

Metadata

Answer 44

Data related to the image file data itself. this includes image properties such as width, height and colour depth.

Question 45

Resolution

Answer 45

A measure of the total number of pixels in an image, typically expressed in terms of the number of dots/pixels per inch.

Question 46

Vector graphics

Answer 46

An image composed from mathematical coordinates and functions (lines and curves).

Question 47

Nyquist theorem

Answer 47

A sufficiently accurate digital waveform of an analogue signal would require a sampling rate of at least twice the highest frequency that appears in the original analogue signal.

Question 48

Sample resolution

Answer 48

The number of bits used to represent a single sample.

Question 49

Sampling rate

Answer 49

The number of samples taken per second.

Question 50

Sound sampling

Answer 50

The process of converting analogue sound waves to a digital waveform, by storing a finite number of readings in binary.

Question 51

Event messages

Answer 51

Binary data transmitted between the MIDI device and computer processor that carries properties controlling when and how sounds are produced.

Question 52

MIDI

Answer 52

Musical instrument digital interface is a protocol for ADC audio transmission to a digital interface used for the majority of electronic musical instruments and computers.

Question 53

Dictionary-based coding

Answer 53

A type of lossless compression where text is searched for entries that match the entries in a dictionary. Entries are substituted by a unique code which can then be translated.

Question 54

Lossless compression

Answer 54

A compression algorithm that retains all the data in the file by only storing the instructions needed to reconstruct the original file. No data is lost.

Question 55

Lossy compression

Answer 55

A compression algorithm that removes non-essential data from a file leading to a noticeable decrease in accuracy of the data. Data lost is non-recoverable.

Question 56

Run-Length encoding

Answer 56

A type of lossless compression where repeated occurrences of the same data (like several pixels of the same colour in an image) are stored as single data values with their counts.

Question 57

Encryption

Answer 57

The process of converting the original data (plaintext) into a form which cannot be understood by unauthorised users (cipher text) using an encryption algorithm (cipher).

Question 58

Caesar Cipher

Answer 58

A substitution cipher where each letter of plaintext is substituted for another that is a fixed number of letters ahead in the alphabet, which becomes the cipher text.

Question 59

Vernam cipher

Answer 59

A cipher that uses a one-time pad (a secret random key) to convert each character to cipher text by modularly adding it with the corresponding character of the key. This is impossible to decrypt without a key.