Data Representation 1.1 - 1.3

Question 1

What is the binary number system?

Answer 1

Base 2 system using only 0 and 1, with place values as powers of 2 (e.g. 128,64,32,16,8,4,2,1 for 8 bits).

Question 2

Why do computers use binary?

Answer 2

Switches are ON (1) or OFF (0), so binary matches computer’s hardware logic gates and storage.

Question 3

How to convert binary to denary?

Answer 3

Add place values (powers of 2) where there is a 1. E.g. 11101110 = 128+64+32+8+4+2 = 238.

Question 4

Denary to binary Method 1?

Answer 4

Successive subtraction of largest possible powers of 2, write 1 if subtractable, 0 if not.

Question 5

What is hexadecimal?

Answer 5

Base 16 system using 0–9 and A–F (A=10, F=15), place values powers of 16.

Question 6

Binary to hex?

Answer 6

Group into 4 bits from right, convert each group (e.g. 1111=F).

Question 7

Hex to binary?

Answer 7

Each hex digit to 4-bit binary (e.g. F=1111).

Question 8

Hex to denary?

Answer 8

Multiply each digit by power of 16, sum (e.g. 45A: 4×256 + 5×16 + 10×1 = 1114).

Question 9

Denary to hex?

Answer 9

Repeatedly divide by 16, remainders bottom to top (10–15 as A–F).

Question 10

What is a MAC address?

Answer 10

48-bit hex identifier for network card: NN-NN-NN-DD-DD-DD (manufacturer + serial).

Question 11

What is an IP address?

Answer 11

Unique network address. IPv4: 32-bit (e.g. 109.108.158.1). IPv6: 128-bit hex groups.

Question 12

How does HTML use hex?

Answer 12

RRGGBB for RGB colours (FF0000=red, 00FF00=green).

Question 13

What are the uses of hexadecimal?

Answer 13

.

Question 14

What are the advantages of using hexadecimal representation?

Answer 14

.

Question 15

How many unique numbers can be represented in a n bit binary number?

Answer 15

2^n

Question 16

What is the largest possible number that can be represented by n bit binary number?

Answer 16

2^n-1

Question 17

what is the smallest and largest 8 bit number that can made in 2s complement? (binary and denary)

Answer 17

.

Question 18

Binary addition rules?

Answer 18

0+0=0 c0; 0+1=1 c0; 1+0=1 c0; 1+1=0 c1 (carry 1).

Question 19

What is overflow in 8-bit addition?

Answer 19

Carry out of MSB when result >255 (e.g. 240+48=288 → overflow). And an extra bit gets generated from the availible bits

Question 20

Logical left shift effect?

Answer 20

Multiplies by 2^n (bits shift left, 0s in from right, MSB lost if overflow).

Question 21

Logical right shift effect?

Answer 21

Divides by 2^n (bits shift right, 0s in from left, LSB lost).

Question 22

What is two’s complement?

Answer 22

Method to represent signed 8-bit integers (−128 to +127). MSB=sign bit.

Question 23

Positive denary to 8-bit two’s comp?

Answer 23

Convert to binary, pad to 8 bits (MSB=0).

Question 24

Negative denary to two’s comp?

Answer 24

Take positive binary, invert bits, add 1.

Question 25

What is extended ASCII?

Answer 25

.

Question 26

Two's comp to denary (negative)?

Answer 26

Take -128 (first bit) and then add the bits to get a denary value (e.g -128 + 32 + 16)

Question 27

E.g. −25 to 8-bit two's comp?

Answer 27

+25=00011001 → invert 11100110 +1=11100111.

Question 28

What is a character set?

Answer 28

List of characters + their binary codes (e.g. ASCII, Unicode).

Question 29

What is ASCII?

Answer 29

7-bit character set (128 codes) for letters, numbers, symbols.

Question 30

What are the advantages of Unicode over ASCII?

Answer 30

ASCII can't represent all languages/symbols; Unicode uses more bits for millions of characters.

Question 31

What is sampling?

Answer 31

Measuring sound wave amplitude at regular intervals to digitise.

Question 32

Sample rate?

Answer 32

Samples per second (Hz). Higher = more accurate time changes, bigger file.

Question 33

Sample resolution/bit depth?

Answer 33

Bits per sample. Higher = more amplitude levels, better quality, bigger file.

Question 34

What is a bitmap image?

Answer 34

Grid of pixels where each pixel has a binary colour value.

Question 35

What is a pixel?

Answer 35

Picture element: smallest unit of image, has colour value.

Question 36

Image resolution?

Answer 36

Width × height in pixels. Higher = more detail, bigger file.

Question 37

Colour depth?

Answer 37

Bits per pixel for colour. 2^n colours. Higher = more colours, bigger file.

Question 38

Pixelated image?

Answer 38

Low resolution shown too large: pixels visible as blocks.

Question 39

Bit?

Answer 39

Single binary digit (0 or 1).

Question 40

Nibble?

Answer 40

4 bits.

Question 41

Byte?

Answer 41

8 bits.

Question 42

KiB?

Answer 42

1024 bytes.

Question 43

MiB?

Answer 43

1024 KiB = 1 048 576 bytes.

Question 44

GiB?

Answer 44

1024 MiB = 1 073 741 824 bytes.

Question 45

GiB?

Answer 45

1024 MiB = 1 073 741 824 bytes.

Question 46

Bitmap file size formula?

Answer 46

(width × height × colour depth in bits) ÷ 8 = bytes.

Question 47

E.g. 2048×2048, 16‑bit colour file size?

Answer 47

Pixels=4 194 304; bits=67 108 864; bytes=8 388 608; MiB=8.

Question 48

Mono sound file size?

Answer 48

Sample rate × resolution (bits) × seconds.

Question 49

Stereo sound adjustment?

Answer 49

Multiply by 2 (two channels).

Question 50

Why compress data?

Answer 50

Reduce file size for faster transmission, less storage, less bandwidth.

Question 51

Lossless compression?

Answer 51

Reduces size without data loss (e.g. RLE). Original fully recoverable.

Question 52

Lossy compression?

Answer 52

Permanently removes data (e.g. reduce resolution). Smaller but quality loss.

Question 53

When use lossy?

Answer 53

Photos/music/video where minor quality loss OK.

Question 54

RLE (run length encoding)?

Answer 54

Replaces runs of identical values with (count, value). Best for repeated data.

Question 55

E.g. RLE for 'AAAAAABBBB'?

Answer 55

(6,A)(4,B).

Question 56

What are the disadvantages of RLE?

Answer 56

.