Fundamentals of Data Representation

Number base

The number of unique digits available in a numbering system

Binary

0, 1 (base 2)

Decimal

0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (base 10)

Hexadecimal

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F (base 16)

Bit (b)

A single binary digit

Example: Either a single '1' or '0'

Byte (B)

A sequence of eight bits

Example: An individual keyboard characters, such as '#' or 'k'

Kilobyte (KB)

1000 bytes

Example: A paragraph of text, containing around 200 words

Megabyte (MB)

1000KB

Example: Around one minute of average quality MP3 music

Gigabyte (GB)

1000MB

Example: Around ninety minutes of standard definition video

Terabyte (TB)

1000GB

Example: Depending on the quality, several hundred hours of video

Binary Shift

Moving the values of a binary number left and right

What does each binary shift do?

Right shift by one place - Divides by 2
Left shift by one place - Multiplies by 2

Character

A single symbol, such as a letter, number, symbol or space

Character set

A list of all characters recognised by a computer system. Examples include ASCII and Unicode

ASCII

American Standard Code for Information Interchange. Can represent characters of the English alphabet as well as numbers and special characters

Uses seven bits, so 128 characters can be represented

Unicode

Uses 16 bits, so 65536 characters can be represented. Gives access to other languages such as Chinese and Russian, as well as emojis. More storage space is required

Pixel

The smallest possible unit within an image or on a screen. Cannot be divided up into smaller units, and can only be one colour at a time

Colour depth

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

Size in pixel

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

Image size equation

In bits: Width x Height x Colour Depth (W x H x D)
In bytes: (W x H x D) / 8

Analogue signal

A continuosly variable signal. It could be one of two values, such as '0' or '1', or anything in between, such as '0.1879'

Is sound analogue or digital?

Sound is an analogue signal, since frequencies do not occur at set points

Why does analogue data need to be converted to digital?

In order to be stored and processed. It is done by taken regular samples of the sound's amplitude

Sampling rate

A measure of how often a sample is taken, measured in Hertz (Hz). A higher sampling rate results in higher accuracy but requires more storage space.

Sample resolution

The number of bits required to store each sample

Sound File size equation

In bits: Sampling rate x Sample resolution x Seconds
In bytes: (Rate x Resolution x Seconds) / 8

Compression

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

Lossless compression

Allows the original data to be exactly reconstructed from compressed data. Used when data needs to be precise

Lossy compression

Causes some data to be lost during the compression process. Typically used in photographs or music, when data does not need to be precise. It can save disk space or transmission time.

Run Length Encoding (RLE)

A form of lossless 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

Uncompressed: QQQQQQQQWWWWWWEEEQQQQQQQQ
Compressed: 8Q6W3E8Q

Huffman Encoding

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