Fundamentals of Data Representation

Question 1

Multiplying unsigned binary integers

Answer 1

11011 x
       11
---------
  11011
110110

Question 2

Two’s Complement

Answer 2

A method of working with signed binary values (positive and negative integers)
http://preview.ibb.co/h0LJEd/E10_EA4_A1_396_C_4_F70_B90_C_76_C8_D9577_C82.jpg

Question 3

Fixed Point

Answer 3

Where the decimal/binary point is fixed within a number.

https://image.ibb.co/nvFSqJ/fixed_point.jpg

Question 4

Floating Point Numbers

Answer 4

Where the decimal/binary point can move within a number.

https://youtu.be/dcIDAnfp8Dc?t=5m21s

Question 5

Advantages of Floating Point over Fixed Point

Answer 5

A wider range of numbers can be produced with the same number of bits as a fixed point.

Question 6

Advantages of Fixed Point over Floating Point

Answer 6

Quicker to process due to no processing required to move the binary point
More precise despite a more limited range of numbers.

Question 7

Normalisation Main Use Case

Answer 7

Storing the number with the greatest accuracy possible

Question 8

How to tell if a number is normalised

Answer 8

If the number is normalised
Positive - binary starts with 01
Negative - binary starts with 10

https://youtu.be/RcY0aiSsyqI?t=3m55s

Question 9

Overflow

Underflow

Answer 9

When a number is too large to be represented with the number of bits allocated.
When a number is too small to be represented with the number of bits allocated.

Question 10

Absolute Errors

Relative Error

Answer 10

The actual mathematical difference between the answer and the approximation of it, that you can store.

Relative Error = Absolute Error / Number intended to be stored

Question 11

Character Code

Answer 11

A binary representation of a particular letter, number or special character.

Question 12

ASCII

Answer 12

A standard binary coding system for characters and numbers

Question 13

Unicode

Answer 13

A standard binary coding system that has superseded ASCII

Question 14

Parity Bit

Answer 14

A method of checking binary codes by counting the numbers of 0s and 1s

Even Parity - If there are an odd number of 1s in a binary code, a 1 parity bit is added to make the number of 1s even. Once the data is received, it is checked to ensure there is an even number of 1s, if there are, dada is assumed to be correct.

Odd Parity 0 If there are an even number of 1s in a binary code, a 1 parity bit is added to make the number odd. Once the data is received, it is checked to ensure there is an odd number of 1s, if there are, dada is assumed to be correct.

Question 15

Majority Voting

Answer 15

A method of checking for errors by producing the same data several times and checking it is the same each time.

1001 would be send as 111 000 000 111
When the data is checked, you would expect to see patterns of 3 bits.

Question 16

Check Digits

Answer 16

A digit is added to the end of binary data to check the data is accurate. It is the most popular method of checking ef used on barcodes. However, it is also the most error-prone method.

The most simplest way to calculate a check digit is to keep on adding digits until it becomes one number:

123456 –> 1+2+3+4+5+6 = 21 –> 2+1 = 3.
Therefore 3 is the check digit.

However, thie problem with this system is that if two numbers are swapped around, the check digit will be the same. To overcome this, each number is given its own weighting. This means each number is multiplied by a different weight or scale factor. A common method is the modulo-11 method:
https://image.ibb.co/hCsMjd/checkdigits.jpg

Question 17

Bit-Mapped Graphs

Answer 17

An image made up of individual pixels

To create colour graphics, each pixel is mapped to more than one bit (eg one byte/8 bits) which means each pixel could be 2^8 or 256 (Colour Depth) different colours

Colour Depth - The number of bits or byted allocated to represent the colour of a pizel in a bit-mapped graphic

Your computer will contain a graphics card for controlling graphics. The amount of memory allocated for bit-mapping depends on the amount of memory on the card.

Storage = resolution x colour depth.

Question 18

Vector Graphics

Answer 18

An image made up of objects and coordinates

Question 19

Analogue and Digital Conversions

Answer 19

Analogue to Digital Converter (ADC) - Microphone and a computer, the microphone inputs sound inthe form of changes in air pressure and then converts them into electrical signals. These analogue electrical signals are then converted by the ADC into digital signals that the computer can process.

Digital to Analogue Converter (DAC)

Question 20

Sound Sampling

Answer 20

Sampling is the process of converting analogue sound waves into digital form to create what is commonly known as digitised or digital sound.

To calculate how large the file size will become you can use the following calculation
sample rate (Hz) * length of recording (secs) * sampling resolution (bits)

eg If sample rate was 44000Hz, with a recording lasting 60 seconds with a sample of 16 bits (two bytes)
44000 * 60 * 16 = 42240000 bits = 5280000 bytes or 5.28MB

Question 21

Data Compression

Answer 21

Compression is the process of encoding information with fewer bits so that the files take up less memory.

Lossless means that the compressed file is as accurate as it was before compression ie no data is lost
Lossy means that there will be some degradation in the data, for example, a grainer image might be produced.

Lossless compression uses run-length encoding for images, which is a method of compressing data by eliminating repeated data. Eg an image contains data about each pixel, so the file read: blue blue, blue, blue, red, red. You could instead store: x blue pixels, then x red pixels so it is compressed without losing quality. eg BBBBBBBBB pixels will simply display 9B for 9 blue pixels.

For text files, lossless compression uses Dictionary-based encoding. For example, many words end in tion, such as station, nation and creation. Rather than storing the words individually, ‘tion’ can instead be encoded to the dictionary as ‘1’ and then used in combination with other prefixed to form words. This significantly reduces file size without losing quality.

Question 22

Encryption

Answer 22

The process of turning plaintext into scrambled ciphertext, which can only be understood if decrypted.

Question 23

Decryption

Answer 23

The process of deciphering encrypted data or messages.

Question 24

The Caesar Cipher

Answer 24

The Caesar Cipher is a substitution cipher where one character of plaintext is substituted for another, becoming the cipher text.
Eg a two-letter shift - A = C, B = D, C = E
Or random substitution - A = O, B = Z, C = P

A further level of complexity can be added to the substitution cipher using polyalphabetic cipher
eg encrypting the letter B
B –> W in 1st alphabet
W –> Q in 2nd alphabet

Polyalphabetic - Using more than one alphabet.

Question 25

Frequency Analysis

Answer 25

In cryptography, it is the study of how often different letters or phrases are used.

Question 26

Transposition Cipher

Answer 26

A transposition cipher is when the letters of the message are transposed, or rearranged to form an anagram.

Railfence Cipher - https://www.thecrazyprogrammer.com/wp-content/uploads/2017/09/Rail-Fence-Cipher-Example.png
Original Message - Hello World
Encrypted message - HorelollWd

Route Cipher - https://bit.ly/2sXkxup

Question 27

Vernam Cipher

Answer 27

Varnam Cipher is known as the one-time pad cipher.
Vernam Cipher is considered to be the most secure method of encryption, unbreakable.

All “one-time pad ciphers” offer perfect security IF:

• The encryption key (one-time pad) is equal to or longer than the plaintext message
• The Key is truly random
• The key is used only once and then destroyed.

How to apply Vernam Cipher:
Get message you want to encrypt
Create one-time pad
Find ASCII binary code for the first letter of both
Perform XOR on each binary code
Find the new ASCII character from the new binary code
Repeat for each character.

Question 28

One-time Pad

Answer 28

A key that is only used once to encrypt and decrypt a message and is then discarded.