3.3- Fundamentals of Data Representation

What is binary?

A number system consisting of only 0's and 1's. Binary can be used to store texts, images, sounds and program instructions.

What is the most/least significant bits?

- Most significant bit (MSB) is the bit with the largest value, the bit furthest to the left.

- Lest significant bit (LSB) is the bit with the lowest value, the bit furthest to the right

What is the unit for bits, bytes, kilobytes, megabytes, gigabytes and terabytes

- Bits (b)
- Bytes (B)
- Kilobytes (kB)
- Megabytes (MB)
- Gigabytes (GB)
- Terabytes (TB)

What is Hexadecimal?

A number system consisting of 10 digits the letters A-F.

1,2,3,4,5,6,7,8,9,10,A,B,C,D,E,F

How many bits is a nibble

4 bits

How many bits is in a byte?

8 bits

List megabyte, terabyte, petabyte, kilobyte and gigabyte (Lowest to Highest)

Kilobyte, Megabyte, Gigabyte, Terabyte, Petabyte

How do you convert 45 to binary?

128 and 64 are too large so they are both 0's. 32 is less than 45 so it is a 1. 45 - 32 is 13 which is less than 16 so the next number is 0. 13 is larger than 8 so it gets a 1, 13 - 8 is 5 so 4 and 1 get 1's and 2 is 0. So the number is:

00101101

How do you convert 10110011 to decimal?

- 128 is a 1 so it is included
- 64 is a 0 so it isn't included
- 32 and 16 are 1 so they are included
- 8 and 4 are both 0 so they aren't included
- 2 and 1 are 1 so they are included

128+32+16+2+1 = 179

How do you calculate the largest integer you can have with the amount of bits given?

Largest Formula = 2^no of bits - 1

E.g. 8 bits:
2^8 - 1 = 255

What is 4F in decimal?

4 x 16 = 64
F = 15
64 + 15 = 79--Ans: 79

What is 79 in Hexadecimal

79/16 = 4.9375 So the first value is 4
4 x 16 = 64
79 - 64 = 15 = F
Ans: 4F

How to convert 8-digit Binary to Hexadecimal

Split into 2 groups of 4
The left side 4 is converted to decimal is the first value.
The right side 4 is converted to decimal and that is the second value.

Convert 01001111 to Hexadecimal

Split into two 4's (0100 and 1111)
Find values of both (0100 = 4)(1111 = 15)
Find hexadecimal values (4 = 4)(15 = F)
So answer = 4F

What are the binary addition rules?

0 + 0 = 0
1 + 1 = 1 (carry the 1)
0 + 1 = 1

What does shifting to the left once in binary do?

multiply by 2

What does shifting once to the right do in binary?

divide by 2

What does ASCII stand for?

American Standard Code for Information Interchange

What is ASCII?

A character set that uses 7 or 8-bit binary values to represent characters (letters, numbers and symbols). Limited to 128 characters.

What is Unicode?

A character set that holds 16-bit binary values (65536 characters) to represent all characters of every language (including ASCII's characters).

What are the differences between Unicode and ASCII?

- ASCII uses 7 or 8-bit binary whereas Unicode uses 16-bit binary.
- Unicode includes every language but ASCII only has english letters, numbers and symbols.

Advantages of Unicode over ASCII

• Greater range of characters, eg emojis

• Includes characters from different languages

What is a pixel?

Single point in an image; // Smallest (addressable) part / bit of an image // A single dot / point of colour

How can a pixel image be converted into a bitmap

1. The pixels are stored consecutively (in memory locations)

2. [x] combinations of bits are possible // each colour could be represented by a unique [x]-bit pattern

3. the bitmap will need the width and height / dimensions and colour depth / bits per pixel to be stored / included

4.metadata would need to be stored

What is an image resolution?

The concentration pf pixels in a specific area. Defined with the width and height in pixels usually.

What is image bit depth? What is the equation?

Number of pixels available to represent colours

x bits per pixel = 2^x colours

What is the image file size calculation?

File Size [bits} = Image width x Image height x Colour depth (/8 if you want in bytes)

What is metadata?

Data that describes data. Information other than the main data that is stored about the file. For example, Date created, Author and Resolution.

What type of wave is analogue sound?

continuous

What type of wave is digital sound?

Discrete (sampled at regular intervals)

What is sample rate?

The number of samples taken per second, measured in Hertz (Hz).

What sample rate are CD's sampled at?

44100Hz or 44.1kHz

What is sample resolution?

The number of bits used to record each measurement. Also called bit depth.

How do you calculate sound file sizes?

File size [bits] = Sample rate x Sample resolution x Duration [seconds] (/8 if you want it in bytes)

What is compression and its 2 types?

Algorithms which reduce file sizes. There are two types of compression:

- Lossy
- Lossless

What are the benefits of compressing files?

- Smaller file sizes
- Fewer packets
- Quicker to complete transmission
- Reduce traffic over the internet
- Data can be sent at the same rate at which it is bein played at

What is lossy image and sound compression?

- Image compression permanently removes data, can result in small mistakes known as digital artifacts
- Sound compression permanently removes sound that we can't hear (too high or low of a frequency). Can negatively affect the sound quality.

What is lossless image and text compression?

- Image compression finds groups of repeating data and records data once along with the number of times it repeats.
- Text compression uses repeated patterns in the original text and encodes the pattern into a dictionary

What is run length encoding (RLE)?

Run Length encoding rather than recording every pixel in an image it records its value and the number of times it repeats.

For example, 11111110000011 can be represented as 7,1 5,0 2,1.

What is Huffman coding?

The frequency with which characters in a body of text are used.

What are Huffman trees?

Character are placed into a binary tree with the most frequently occurring characters being placed at the top of the tree and the lower being at the bottom.

What is buffering?

This is when the download speed is slower than the playback speed.