3 - Fundamentals of Data Representation

Question 1

Number base

Answer 1

The number of unique digits available in a numbering system. E,g: In decimal these are 10 individual digits available (0,1,2,3,4,5,6,7,8,9), so it is also known as base 10

Question 2

Computer binary

Answer 2

Computers use binary to represent all data and instructions. Whatever a user enters, be it number, text, image, sound, or video, it is ultimately stored as a string of 0’s and 1’s

Question 3

Binary to decimal conversion

Answer 3

Use the table thing: 128 64 32 16 8 4 2 1

Place binary underneath and add to number

E.g: 11001010 = 202
since 128 + 64 +8 + 2 = 202

Question 4

Decimal to binary conversion

Answer 4

Put 1 into biggest number it can go into, then do the same going down the 128 number thing

E.g: 85 = 01010101

Question 5

Hexadecimal

Answer 5

One hexadecimal digit can always be translated to four binary digits. Hexadecimal is used as shorthand, since it is quicker to write and less prone to being misread

Question 6

Hexadecimal examples table

Answer 6

Binary : Decimal : Hex

0000 : 0 : 0
0001 : 1 : 1
1001 : 9 : 9
1010 : 10 : A
1111 : 15 : F

Question 7

To convert from binary to hexadecimal

Answer 7

1. We’re gonna convert 011110 to decimal
2. If binary number has a number of digits divisible by 4 (e.g: 4,8,12, etc) it can be left alone. Else add 0’s to left until the number of digits is div by 4. We add 2 0’s to left to our number
3. Next split the number into ‘nibbles’ of four bytes each
4. Finally convert each nibble separately, using the hex table
   011110
   00011110
   0001 1110
   0001 = 1
   1110 = E

So 011110 = 1E

Question 8

To convert hexadecimal to binary

Answer 8

1. We’re gonna convert A6
2. Each hex digit translate to binary nibble, use table
3. Attach nibbles together

A6
A = 1010
6 = 0110
1010 0110

So A6 = 10100110

Question 9

To convert between decimal and hexadecimal numbers

Answer 9

Best way is to go through a binary number

So either
- Decimal > Binary > Hex
Or
- Hex > Binary > Decimal

Question 10

Bit (b)

Answer 10

A single binary digit // Either a single ‘1’ or ‘0’

Question 11

Byte (B)

Answer 11

A sequence of 8 bits // An individual keyboard character such as ‘#’ or ‘k’

Question 12

Kilobyte (KB)

Answer 12

Approx 1,000 bytes // A paragraph of text containing around 200 words

Question 13

Megabyte (MB)

Answer 13

Approx: 1,000 KB or
1,000,000 B
// Around 1 min of average quality mp3 music

Question 14

Gigabyte (GB)

Answer 14

Approx: 1,000 MB or
1,000,000 KB or
1,000,000,000 B
// About 90 mins of standard definition video

Question 15

Terabyte (TB)

Answer 15

Approx: 1,000 GB or
1,000,000 MB or
1,000,000,000 KB or
1,000,000,000,000 B
// Depending on quality - several hundred hours of video

Question 16

Binary Shift

Answer 16

Moving values of a binary number left or right

a. 00011000 > Shift right 1 > 00001100
b. 00001100 > Shift left 2 > 00110000

Question 17

Shifting loss/gain

Answer 17

When you shift left or right, any bits that ‘fall off’ the end are lost forever; any bits that join the number at the other end are always ‘0’

Question 18

Shifting

Answer 18

Shift Left:
Shift 1: X2
Shift 2: X4
Shift 3: X8

Shift Right:
Shift 1: Div 2
Shift 2: Div 4
Shift 3: Div 8

Question 19

Adding binary

Answer 19

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (10 is binary for 2, need to carry)
1 + 1 + 1 = 11 (11 is bianry for 3, and you will need to carry

Question 20

10110101 + 00111100

Answer 20

1. Stack the numbers
2. Add the pairs
3. Result should be 11110001

Question 21

Character

Answer 21

A single symbol, such as a letter, number, symbol or space. Most keys on a keyboard cause one character to appear on screen

Question 22

Character set

Answer 22

A list of all characters recognised by a computer system. Each character has a corresponding code, and the same codes are used by all computers that use the same character set. ASCII (American Standard Code of Information Interchange) and Unicode are two common character sets

Question 23

Character, ASCII and Unicode

Answer 23

Character Value : ASCII : Unicode

A : 100 0001 : 0000 0000 0100 0001
a : 110 0001 : 0000 0000 0110 0001
# : 010 0011 : 0000 0000 0010 0011
3 : 011 0011 : 0000 0000 0011 0011

Question 24

Character groups

Answer 24

Characters are commonly grouped and run in the order that you would expect, i.e. ‘A’ in ASCII has a decimal representation of 65. ‘B’ is 66, ‘C’ is67, ‘D’ is 68, etc. In lower case, ‘a’ is 97, ‘b’ is 98, ‘c’ is 99, etc. Numerals (0, 1, 2, 3, etc.) are similarly grouped together

Question 25

Character set bits

Answer 25

ASCII uses seven bits, meaning 128 different characters (27) can be represented.

Unicode uses sixteen bits, meaning 65,536 different characters (216) can be represented. Using Unicode instead of ASCII gives you access to far more alphabets, including Chinese, Japanese, Arabic and Russian, but more storage space is required

Question 26

Representing Images

Answer 26

An image is divided into pixels, each of which is a tiny dot on screen. A pixel can only be one colour at a time, and when a picture is saved, the colour of each individual pixel must be stored in binary. The more bits that are used to store each pixel, the more colours are potentially available

Question 27

Pixel

Answer 27

Short for picture element, this term refers to the smallest possible unit within an image or on a screen. A pixel cannot be divided up into smaller units, and a pixel can only ever by one colour at a time. VDUs display output using millions of pixels

Question 28

More bits?

Answer 28

If more colours are needed, more bits are needed. Many images store 24 bits, three bytes, for each pixel

Question 29

Amount of storage required

Answer 29

The amount of storage required for an image depends on a number of factors including:

• Colour depth
• Size in pixels

Question 30

Colour depth

Answer 30

A measure of how many colours are available; the more colours that are available, the more bits that must be assigned to store each pixel

Question 31

Size in pixels

Answer 31

The number of pixel in height and width for an image. More pixels require more storage space than a lower-res image, but result in an image of higher quality

Question 32

Calculating Image size

Answer 32

W - width of img (in px)
H - Height of img (in px)
D - Colour depth, n.o of bits used to store each pixel

File size in bits: W x H x D
File size in bytes: (W x H x D) / 8

Question 33

Convert file size from B to KB or B to MB

Answer 33

Bytes to Kilobytes:
Divide the number of bytes by 1,000

Bytes to Megabytes:
Divide the number of bytes by 1,000,000

Question 34

Analogue

Answer 34

Sound is an analogue signal, which is the opposite of digital. A comp usually works with digital signals, processing 0s and 1s. An analogue signal is continuously variable. It might be one of two values, such as 1 or 0, or anything in between, such as 0.817. Sound is an analogue signal, since frequencies do not occur at set points

Question 35

To process sound

Answer 35

Analogue data needs to be converted to digital in order to be stored and processed. This is done by taking regular samples of the sound’s amplitude. With sound, thousands of samples are taken per second, each being a measure of the amplitude at a specific point in time

Question 36

Sample rate

Answer 36

A measure of how often a sample is taken, measured in Hertz (Hz). 1 Hz means once per second, 1MHz means one million times per second. A sound wave with more samples per second has a higher sampling frequency

Question 37

High Sampling Rate

Answer 37

A high sampling rate results in higher accuracy but requires more storage space

Question 38

Sample resolution

Answer 38

Not to be confused with screen resolution, which is a measure of the number of pixels. Resolution is sound sampling refers to how many bits are required to store each sample

Question 39

Calculating sound file size

Answer 39

Sampling rate - Number of samples per sec
Sample res - Number of bits used to store each sample
Seconds - the length, in seconds, of the whole sound file

File size in bits: Rate x Res x Seconds
File size in bytes: (Rate x Res x Seconds) / 8

Question 40

Compression

Answer 40

Techniques to reduce the size of a file, so that it takes up less storage space and can be transmitted across a network more quickly. There are different types of compression

Question 41

Choice of compression

Answer 41

Choice of compression type might depend on a number of factors:

• If data needs to be precise, such as in money transactions, lossless compression would be used
• If data does not need to be precise, typically as in photos or music, lossy compression might be considered to save disk space and transmission time

Question 42

Run length encoding (RLE)

Answer 42

A form of compression that is effective when dealing with repeating data. Instead of storing each item of repeated data, the data is stored once, along with how many times it repeats

Question 43

What RLE does

Answer 43

• Is lossless compression

Effective in storing or transmitting a file that contained lost of repeated data such as:

• a txt file that contains repeated characters e.g: zzzzz
• An img file where lots of adjacent px are identical colour
• Sound file containing stretches of complete silence

Question 44

RLE example

Answer 44

Uncompressed: QQQQQQQQWWWWWWEEEEEEEEEEEEEEEQQQQQQQQ
Compressed: 8Q6W15E8Q

Question 45

RLE larger file

Answer 45

Uncompressed: QWERTY
Compressed: 1Q1W1E1R1T1Y

Because no letters were repeated in the uncompressed file, the ‘compression’ process has actually resulted in a larger file

Question 46

Huffman encoding

Answer 46

a form of compression that represents commonly used characters with smaller bit patterns, and rarely used characters with larger bit patterns

Question 47

Huffman example

Answer 47

To write ‘razzmatazz’, using this encoding, the following bit strings would be used in order:
110 10 0 0 1110 10 111 10 0 0
or
110100011101011111000

An ASCII representation of the word ‘razzmatazz’ would have required 70 bits (10 chars x 7 bits per char). The Huffman encoded representation requires on 21 bits. Coz the most commonly used char ‘z’, is given the shortest code ‘0’. Ofc much of this saving would be lost due to the fact that the Huffman tree itself would also need to be transmitted. However, for larger amounts of txt, a substantial saving can be made in terms of file size, even when the size of the tree is factored in