5. Fundamentals of Data Representation

Question 1

Define the following types of number, giving examples: Natural, Integer, Rational, Irrational, Real

Answer 1

Natural - the set of positive whole numbers starting at zero, {0, 1, 2, 3, 4…}
Integer - the set of positive and negative whole numbers, {… -3, -2, -1, 0, 1, 2, 3…}
Rational - the set of numbers which can be expressed as a fraction, {1/2, 1/3, 2/3…}
Irrational - the set of numbers which cannot be expressed as a fraction, e.g. π = 3.14159265359…
Real - the set of all non-Complex numbers including the Naturals/Integers/Rationals/Irrationals.

Question 2

What is an Ordinal Number?

Answer 2

An Ordinal Number identifies a position. Ordinal Numbers are used as indexes into Arrays and Lists.

Question 3

What is Binary?

Answer 3

Binary is the representation of data using 0’s and 1’s. If a number is being represented this is called Base-2.

Question 4

What is Hexadecimal?

Answer 4

Hexadecimal is the representation of numbers using Base-16. Hexadecimal is commonly used as a compact representation of large numbers. For example Hexadecimal is used to represent colours, and memory addresses.

Question 5

Define the following data units: bit, byte, Kilobyte (Kb), Kibibyte (Kib), Megabyte (Mb), Mebibyte (Mib), Gigabyte (Gb), Gibibyte (Gib), Terabyte (Tb), Tebibyte (Tib).

Answer 5

bit - a single 0 or 1
byte - 8 bits
Kilobyte (Kb) - 1000 (10^3) bytes
Kibibyte (Kib) - 1024 (2^10) bytes
Megabyte (Mb) - 1,000,000 (10^6) bytes
Mebibyte (Mib) - 1,048,576 (2^20) bytes
Gigabyte (Gb) - 1,000,000,000 (10^9) bytes
Gibibyte (Gib) - 1,073,741,824 (2^30) bytes
Terabyte (Tb) - 1,000,000,000,000 (10^12) bytes
Tebibyte (Tib) - 1,099,511,627,776 (2^40) bytes

Question 6

What is the difference between a Signed and Unsigned number?

Answer 6

A Signed number can store both positive and negative values, an Unsigned number can only store positive values.

Question 7

What is ASCII?

Answer 7

ASCII is the American Standard Code for Information Interchange. It is an encoding of American English characters using a 7-bit Binary encoding. The last bit is used as a Parity Bit. Extended-ASCII uses all 8-bits for encoding a character, doubling the number of available characters.

Question 8

What is Unicode?

Answer 8

Unicode is a character encoding which builds on ASCII by supporting non-American text by using more bits per character. There are 8-bit (UTF-8), 16-bit (UTF-16) and 32-bit (UTF-32) versions.

Question 9

What is Error Detection/Checking?

Answer 9

Error Detection/Checking is a family of techniques which are used to identify whether transmitted data has become corrupted in transmission. Examples include Parity Bits and Checksums.

Question 10

What is Error Correction?

Answer 10

Error Correction is a family of techniques which are used to correct detected errors in transmission. An example is Majority Voting.

Question 11

How are Parity Bits used?

Answer 11

Parity Bits are a form of Error Detection.

Before transmission of data the sender and receiver will agree on whether to use Odd Parity or Even Parity. The Parity Bit is set so that the number of 1’s in the transmitted data are odd (Odd Parity) or even (Even Parity). When the data is received the number of 1’s is counted and if they don’t match the agreed Parity then an error must have occurred in transmission.

Parity Bits can only be used to detect an odd number of bits flipping, if an even number of bits flip then the Parity will be unaffected.

Question 12

How does Majority Voting work?

Answer 12

Majority Voting is a form of Error Detection and Correction.

The sender will send an odd number of repetitions of the same message to the receiver. For each bit in the message there will be several received bits, if they are not all the same then an error must have occurred in transmission and the majority in the received bits will be used (1 if more received 1’s, 0 if more 0’s).

Question 13

How are Checksums used?

Answer 13

Checksums are used for Error Detection.

A Checksum is a value (number) calculated using a mathematical function (a Hash Function) from the data to be transmitted. The Checksum is sent to the receiver along with the data. The receiver then applies the same mathematical function to the received data, and if the calculated Checksum matches the received Checksum then no error has occurred in transmission.

Question 14

What is a Check Digit?

Answer 14

A Check Digit is a similar technology to a Checksum. It is a number calculated from the numbers in a Barcode used to determine whether or not the Barcode has been read correctly by the Scanner.

Question 15

Define the following terms related to Bitmap Images: Pixel, Resolution, Colour Depth.

Answer 15

Pixel (Picture Element) - the colour at a grid location in an image.
Resolution - the number of Pixels in an image (width x height).
Colour Depth - the number of bits used to represent the colour of a Pixel.

Question 16

How do you calculate the size in data of a Bitmap Image?

Answer 16

Resolution x Colour Depth = Width x Height x Bits Per Pixel

Question 17

What is Metadata?

Answer 17

Metadata is data associated with a file which contains information about that file. Examples of Metadata might be: author, creation date, software used, GPS location.

Question 18

How is a Vector Image different from a Bitmap Image?

Answer 18

A Vector Image consists of data which describes the constituent elements (shapes) in the image. This is a parameterised representation of an image where different shapes will have different parameters to represent their location, size, geometry, and colour. For example a circle could be represented by the location of its center, its radius, and the colour. A Vector Image must be rasterised into a Bitmap Image to be displayed on the screen. Vector Images scale much better than Bitmap Images, but are poor at representing photographic images.

Question 19

Define the following terms related to Sampled Sound: Sample Rate, Sample Resolution.

Answer 19

Sample Rate - the number of samples per second of audio.
Sample Resolution - the number of bits per sample of audio.

Question 20

How do you calculate the size in data of a Sampled Sound?

Answer 20

Sample Rate x Sample Resolution x Length of Sound

Question 21

What does Nyquist’s Theorem say about recording Sampled Sound?

Answer 21

Nyquist’s Theorem states that the Sample Rate must be chosen to be at least double the highest frequency that exists in the audio to be recorded.

Question 22

What is MIDI?

Answer 22

MIDI is the Musical Instrument Digital Interface. MIDI is a parameterised representation of music which can be used to transmit and synthesise music. Parameters may represent properties such as the instrument, pitch, duration, tempo, volume etc.

Question 23

What is Compression? How do Lossy and Lossless Compression differ?

Answer 23

Compression is a family of techniques which reduce the size of data. Compression is important for saving system resources (Hard Disk space), and increasing the speed of data transmission over Networks.

Lossy Compression will lose some quality in the original data when compressing, but usually creates a higher Compression ratio (i.e. smaller files). The lost data may be exhibited as artifacts in image files. Lossless Compression loses none of the quality of the original data, but has a lower Compression ratio.

Question 24

How does Run Length Encoding Compress data?

Answer 24

Run Length Encoding (RLE) is used to compress data which has consecutive repetitions of the same symbol. It represents the data as a series of symbols and the number of times they repeat. For example the data:

AAAAAAAABBBBBBBCCCAAAAAABBCCCC

would be encoded as:

A8B7C3A6B2C4

Data, such as text, which does not have many consecutive repetitions will not compress well with RLE.

Question 25

How does Dictionary Compression Compress data?

Answer 25

Dictionary Compression is used to compress data which has repeating words (like text). The words are stored in a Dictionary, with each word allocated a unique numeric index. The text is then replaced by a sequence of indexes into the Dictionary. This will compress the text if words repeat often.

Question 26

What is Encryption? What is the difference between Symmetric and Asymmetric Encryption?

Answer 26

Encryption is a family of techniques used to hide the content of a message from third parties. Symmetric Encryption uses the same Encryption Key both for encrypting and decrypting the message. Asymmetric Encryption uses a different Encryption Key for encrypting than for decrypting the message. Symmetric Encryption requires the sender to pass the key to the receiver, when it may be intercepted, this is called the Key Exchange Problem.

Question 27

How does the Caeser Cipher work?

Answer 27

A Caeser Cipher is a shift cipher which changes each character by moving a certain number of characters to the left or right. The number of places to move each character is the Encryption Key, and this is a type of Symmetric Encryption. For example, the text ‘Hello World’ shifted by 3 characters would give the ciphertext ‘Khoor Zruog’.