Integers (ℤ): The set of numbers with no fractional part. The natural numbers are a subset of the integers. ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}
Rational Numbers (ℚ): The set of numbers that can be expressed as the ratio of two integers. The integers are a subset of the rational numbers since all integers can be expressed as a ratio with 1. ℚ = {0, ½, 0.75, 0.111111…, 300.5, -42, ...}
Real Numbers (ℝ): The set of numbers that can represent real world quantities and have an imaginary part of 0. Rational and irrational numbers are all members of the real numbers. ℝ ={𝜋, 1.5, -7, ¾, 2, 100000000, -11.3432, ...}
Ordinal Numbers: Natural numbers used to describe numerical position or order of objects.
Binary: A number system that only uses ones and zeros to represent numbers (a base 2 system).
Decimal: A number system that only uses 10 characters (0 to 9) to represent numbers (a base 10 system).
Hexadecimal: A number system that only uses 16 characters (0 to 9 and A to F) to represent numbers (a base 16 system).
Number Base: The number of unique digits used by a particular number system to represent numbers.
Bit: A binary digit used by computers as the fundamental unit of information.
Binary Prefix: A prefix to a unit representing a power of 2.
Decimal Prefix: A prefix to a unit representing a power of 10.
Signed Binary: A binary number system that can represent both positive and negative numbers.
Unsigned Binary: A binary number system that can only represent positive numbers
Two’s Complement: A coding scheme used in signed binary to represent negative as well as positive numbers. A negative number is represented by flipping all its digits and adding 1 to the most significant bit.
Fixed Point Form: A form used to represent numbers with a fractional part in any number system. Digits after the fixed point are multiplied by the base raised to a negative power.
ASCII: A character set used to represent alphanumeric characters or symbols as a set of 8 bits.
Unicode: A character set that is a superset of ASCII. It is used to represent alphanumeric characters or symbols as an integer code point which is equal to the character’s ASCII code.
Check Digits: A method of checking codes for errors during data transmission by adding an extra digit to the end (usually calculated/processed from digits in the code itself) that checks whether the data is accurate.
Majority Voting: A method of checking binary codes for errors during data transmission by sending each bit multiple times, in a set. The receiver takes the value with most occurrences in a set as the value for that bit.
Parity Bits: A method of checking binary codes for errors during data transmission by counting the number of ones and zeroes present.
Analogue Data: Data whose values can vary continuously and take on any value between two extremes.
Analogue Signals: A transmission of a set of analogue data structures, that varies with time, between computational processes.
Analogue to Digital Converter (ADC): An integrated circuit capable of converting continuous analogue data to discrete digital data for a computer.
Digital to Analogue Converter (DAC): An integrated circuit capable of converting discrete digital data from a computer to continuous analogue data.
Bitmapped Graphics: An image composed of an array of pixels each with an allocated number of bits, arranged to form an image. Also known as raster graphics.
Colour Depth: A measure of the amount of colour used in an image, expressed in terms of the number of bits per pixel.
Image Size: The total number of pixels in an image expressed in terms of its dimensions: (width in pixels) × (height in pixels).
Metadata: Data related to the image file data itself. This includes image properties such as width, height and colour depth.
Resolution: A measure of the total number of pixels in an image, typically expressed in terms of the number of dots/pixels per inch.
Nyquist theorem: A sufficiently accurate digital waveform of an analogue signal would require a sampling rate of at least twice the highest frequency that appears in the original analogue signal.
Sample Resolution: The number of bits used to represent a single sample.
Sampling Rate: The number of samples taken per second.
Sound Sampling: The process of converting analogue sound waves to a digital waveform, by storing a finite number of readings in binary.
Event Messages: Binary data transmitted between the MIDI device and computer processor that carries properties controlling when and how sounds are produced.
Lossless Compression: A compression algorithm that retains all the data in the file by only storing the instructions needed to reconstruct the original file. No data is lost.
Lossy Compression: A compression algorithm that removes non-essential data from a file leading to a noticeable decrease in accuracy of the data. Data lost is non-recoverable.
Ren-Length Encoding: A type of lossless compression where repeated occurrences of the same data (like several pixels of the same colour in an image) are stored as single data values with their counts.
Encryption: The process of converting the original data (plaintext) into a form which cannot be understood by unauthorised users (ciphertext) using an encryption algorithm (cipher).
Caesar Cipher: A substitution cipher where each letter of plaintext is substituted for another that is a fixed number of letters ahead in the alphabet, which becomes the ciphertext.
Vernam Cipher: A cipher that uses a one-time pad (a secret random key) to convert each character to cipher text by modularly adding it with the corresponding character of the key. This is impossible to decrypt without a key.