3.3 Fundamentals of data representation

Decimal – base 10

The decimal number system (base 10) uses 10 different numerals 0,1,2,3,4,5,6,7,8,9

Binary – base 2

The binary number system (base 2) uses 2 different numerals 0,1

Hexadecimal – base 16

Hexadecimal is a number base that uses the numerals 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F It has a close link to binary as 4 bits can be represented by 1 hexadecimal digit. Hexadecimal is a more compact form than binary and therefore can take up less space on a display and take less time to enter. Note: hexadecimal does not take up less memory space (as a computer only stores binary)

Bit

The fundamental unit of information (a 1 or a 0).

Byte

A group of 8 bits.

Kilo

1000 bytes (103 bytes)

Mega

1000 Kilo (106 bytes)

Giga

1000 Mega (109 bytes)

Tera

1000 Giga (1012 bytes)

Logical binary shift

A logical binary shift involves moving the bits of a binary number to the left or right. Vacated positions are filled by zeros. A shift to the left corresponds to multiplying by 2. A shift to the right corresponds to dividing by 2.

ASCII

ASCII is a character encoding system that uses a 7-bit notation that allows for the representation of 128 unique characters.

Unicode

Introduced to support a wider range of characters due to increased communication across countries. One of the latest standards defines around 155000 characters. It can be encoded in a variety of ways with up to 32 bits per character.

Character set

A collection of characters (letters, numbers, symbols, etc.) that a computer system can process and use to represent text, with each character assigned a unique numerical code.

Pixel

The term pixel stands for picture element. A pixel is a single point of colour in an image.

Bitmap

A bitmap is where images are broken down into a rectangular grid of pixels. Each pixel will have its own colour value.

Analogue

Continuous data – can take any value in a given range. Between any two analogue values there is another value.

Digital

Digital data has discrete values. There are gaps (jumps) between digital data values.

ADC – analogue to digital convertor

An ADC takes samples of the analogue signal at regular intervals. The amplitude of each sample is approximated to an integer value. Each sample is encoded as a binary value.

Sampling rate

A measure of the number of samples taken per second from an analogue signal to create a digital signal.

Sample resolution

A measure of how many bits are used to represent each sample.

Data compression

The process of reducing the storage space required for data by encoding the data using fewer bits than the original representation.

Huffman coding

Huffman coding is a lossless method of data compression. Huffman coding produces variable-length codes where the length of the code depends on the frequency with which a symbol appears in the original data.

Run-length encoding (RLE)

Run-length encoding is a lossless method of data compression. Sequences of identical data values are replaced with a single data value and the count of its repetitions.