Topic 2: Data

Question 1

Why Binary?

Answer 1

Computers contain billions of transistors. These act as switches that have two states: on and off. These states are then represented in binary by 1(on) or 0(off). These are called bits.

Question 2

Binary naming

Answer 2

Bits ( 1 bit)
Nibble ( 4 bits)
Byte (8 bits)

Question 3

An arithmetic expression to show that 256 different colours can be represented in 8 bits

Answer 3

2¡(nr of bits) –> 2¡8

Question 4

How to convert 6 to binary

Answer 4

0 1 1 0

Question 5

Convert 78 into binary

Answer 5

0 1 0 0 1 1 1 0

Question 6

1101 1001 into denary

Answer 6

128—64—-32—-16—–8—–4—–2—–1
——————————————————
1——1—–0——1——1—–0—–0—–1
——————————————————
128 + 64 + 6 + 8 + 1 = 217

Question 7

Two’s complement signed integers

Answer 7

-Remove the - sign
-Convert the number to binary
-Flip the bits
-Add 1

Question 8

How to represent -4 in binary

Answer 8

0 1 0 0 (convert +4 to binary)
1 0 1 1 (flip the bits)
1 1 0 0 (add 1)

Question 9

Binary addition

Answer 9

0 + 0 = 0
0 + 1 = 1
1 + 1 = 0 and carry 1

Question 10

Logical shift left by 2 places: 0001 0100

Answer 10

0101 0000

Question 11

Logical shift right by 3 places: 1011 1000

Answer 11

0001 0111

Question 12

Arithemtic shift right by 1 place: 1000 1000

Answer 12

1100 0100

Question 13

Overflow

Answer 13

when an operation produces a result which requires more bits than available to store result

Question 14

Consequences of overflow

Answer 14

Programs may crash or produce unreliable or incorrect results

Question 15

1 reason why the result of adding 16 bit patterns must be 16 bit in length

Answer 15

The registers inside the machine that hold the original patterns are fixed in width, and so no more that 16 bits can be held.

Question 16

Hexadecimal (10-16)

Answer 16

A-F

Question 17

Convert C3 to binary

Answer 17

1) Each hexadecimal digit is converted to denary (C = 12) and 3)
2) Each denary number is converted into a nibble (1100)(0011)
3) The nibbles are combined to five the binary number (1100 0011)

Question 18

ASCII in python

Answer 18

ord() returns the ASCII code in denary (“c”)–> 99
chr() returns the character for a denary code 100–> (“d”)

Question 19

Upper case characters

Answer 19

65-90

Question 20

Lower case characters

Answer 20

97-122

Question 21

Digits 0 to 9

Answer 21

48-57

Question 22

Image file size equation

Answer 22

W (width) * H (height) * D (colour depth)

Question 23

Pixel

Answer 23

• PICture ELement
• Each pixel has its own individual colour
• The greater the number of pixels, the greater the detail

Question 24

Colour depth

Answer 24

the number of bits used to encode the colour of each pixel

Question 25

Resolution

Answer 25

- number of pixels per inch when - e.g on a monitor or on paper

Question 26

calculate size of image with: - 24-bit colour depth - 410 * 270 pixels in (MiB)

Answer 26

(410 x270x24) / (8x1024x1024)

Question 27

2 Factors that affect quality of a digital image

Answer 27

- Nr of pixels that make it up (more pixels more resolution) - Nr of bits used to encode the colour of each pixel (more bits used, more colours can be displayed)

Question 28

Sample interval

Answer 28

samples of a sound wave taken at regular fixed intervals

Question 29

Sample rate

Answer 29

number of samples over a given time period

Question 30

Analogue recordings

Answer 30

convert the changes in air pressure into voltage changes

Question 31

Audio file size equation

Answer 31

file size (bits) = sample rate * bit depth * recording length (seconds)

Question 32

CDs sample rate

Answer 32

44 100 per second (44.1 kHz)

Question 33

Blu-ray sample rate

Answer 33

96 000 per second (96 kHz)

Question 34

CDs important info

Answer 34

They are recorded in STEREO and so have two channels. Total file size needs to be doubled

Question 35

Calculate size in MiB digital audio file of - 3 minutes - 44.1 kHz sample rate - 16 bits of bit depth

Answer 35

(44 100 * (3*60) * 16) / (8 * 1024 * 1024)

Question 36

Why analogue signal is never fully reproducible

Answer 36

It is recorded at fixed intervals (sample frequency) Therefore the entire analogue signal is not represented in the digital recording.

Question 37

Nr of values of unsigned integers

Answer 37

4 bits (0 to 15) 8 bits (0 to 255)

Question 38

Nr of values of signed integers

Answer 38

4 bits (-7 to 8) 8 bits (-127 to 128)

Question 39

One reason that a 5-bit colour depth is needed to store 24 colours in an image

Answer 39

because 2¡4 = 16, which is less than 24 and 2¡5 = 32, which is the next largest power of 2 greater than 24

Question 40

Conversion units

Answer 40

Byte Kibibyte (KiB) Mebibyte (MiB) Gibibyte (GiB) Tebibyte (TiB)

Question 41

How to convert units

Answer 41

multiply or divide by 1024

Question 42

32 GiB to bits

Answer 42

32 * 1024 * 1024 * 1024 * 8

Question 43

Lossless compresion

Answer 43

- Reduces file sizes without deleting any data - Nothing is lost

Question 44

Lossy compression

Answer 44

- Reduces file size by deleting some data. - The original can never be reconstituted (it has been irreversibly changed)

Question 45

How is lossless compressed?

Answer 45

- Looks for redundancy where the same data is stored many times and groups this data into one reference

Question 46

How is lossy compressed?

Answer 46

- In image files, algorithms analyse the image and find areas where there are only slight differences. These are given the same value and the file can be rewritten using fewer bits. - In digital sound recordings, very small variations in frequency, tone and volume are removed to reduce the file size as the human ear cannot detect these small differences.

Question 47

Uses of lossless compression

Answer 47

- Text files - Graphic files with a low colour depth

Question 48

Uses of lossy compression

Answer 48

- Image files - DIgital sound recordings

Question 49

Less successful uses of lossles compression

Answer 49

- Audio files - 24-bit colour files

Question 50

Less successful uses of lossy compression

Answer 50

- Text files - Executable software

Question 51

Examples of lossless compression

Answer 51

- Compressed text files - GIF and PNG image files - FLAC and ALAC audio files

Question 52

Examples of lossy compression

Answer 52

- MP3 audio files - JPG image files

Question 53

Advantages of file compression :

Answer 53

- less internet bandwidth - transfer time is faster - less storage - reduce congestion on the internet - audio and video files can be streamed

Question 54

Differences between lossy and lossless

Answer 54

In lossy: - when uncompressed it is not exactly the same as the original - for example audio files (MP3) or image files (JPG) In lossless: - when uncompressed, it is restored completely as the original - for example compressed text files