Data Representation and Number Systems

Flashcards covering key vocabulary and concepts from the lecture notes on Data Representation and Number Systems.

Natural Numbers

A set of numbers containing all positive whole numbers and zero; used for counting.

Integers

A set of positive or negative whole numbers, including zero.

Rational Numbers

Numbers that can be expressed as a fraction or decimal; can be positive or negative, including zero.

Irrational Numbers

Numbers that cannot be written as a fraction.

Real Numbers

The set of all possible real-world quantities, including integers, natural, rational, and irrational numbers.

Ordinal Numbers

Integers used to describe the numerical positions of objects in relation to others (e.g., 1st, 2nd, 3rd).

Decimal (Base 10)

The number base humans use, also called denary, using the digits 0-9.

Binary (Base 2)

A number system that uses only two characters, 1 or 0, representing a high or low current in computers.

Hexadecimal (Base 16)

A number system that uses the digits 0-9 and the characters A-F to represent the decimal numbers 0-15; it is the most compact representation.

Bit

The smallest unit of information, taking the values 0 and 1.

Byte

A collection of 8 bits.

Nibble

Half a byte, consisting of 4 bits.

Unsigned Binary

Binary numbers that can only represent positive numbers.

Signed Binary

Binary numbers that can represent both positive and negative numbers.

Two's Complement

A method computers use to perform subtraction by adding negative numbers.

Fixed Point Binary

A way of representing numbers with a fractional part where a specified number of bits are placed before and after the binary point.

Floating Point Binary

A way of representing numbers with a fractional part using a mantissa and an exponent.

Absolute Error

The exact amount by which a value is incorrect.

Relative Error

A measure of uncertainty in a given value compared to the actual value; relative to the size of the given value.

Normalization

Ensuring that floating-point numbers start with 01 for a positive number and 10 for a negative number, providing maximum precision.

Underflow Error

An error that occurs when there are very small numbers to be represented, but there are not enough bits available.

Overflow Error

An error that occurs when the number is too large to be represented with the available bits.

Character Code

A decimal digit used to represent a character in computers.

Unicode

An information coding system introduced in 1991 that allows representation of a wide variety of alphabets by computers.

Parity Bit

A single bit added to a transmission that can be used to check for errors in the transmitted data.

Majority Voting

An error checking method where each bit of data is transmitted multiple times, and the most commonly occurring value is taken to be correct.

Checksum

A value added to the transmitted data, determined by the data itself, used for error detection.

Check Digit

A type of checksum in which only a single digit is added to the transmitted data.

Analogue Data

Data that is continuous and has no limits to the values it can take.

Digital Data

Data that is discrete and can only take certain values.

DAC (Digital to Analogue Converter)

A device used to convert digital signals to analogue signals.

ADC (Analogue to Digital Converter)

A device used for converting analogue signals to digital signals by sampling at regular intervals.

Bitmapped Graphics

Images broken down into pixels, each assigned a specific binary value.

Vector Graphics

Images represented using mathematically created geometric objects and shapes.

Sampling Rate

The number of samples per second in digital representation of sound, expressed in Hertz.

Sample Resolution

The number of bits allocated to each sample in digital representation of sound.

Nyquist Theorem

States that the sampling rate of a digital audio file must be twice the frequency of the sound.

MIDI (Musical Instrument Digital Interface)

Used with electronical musical instruments connected to computers, storing sound as a series of event messages.

Lossy Compression

Compression where some information is lost in the process.

Lossless Compression

Compression where there is no loss in original quality.

Run Length Encoding (RLE)

Reduces file size by removing repeated information and replacing it with one occurrence followed by the number of repetitions.

Dictionary-Based Methods

Compression method where a dictionary containing repeated data is appended to the file.

Encryption

The process of scrambling data so that it cannot be understood if intercepted.

Plaintext

Unencrypted, readable information.

Ciphertext

Encrypted, unreadable information.

Caesar Ciphers

Ciphers that decrypt information by replacing characters, where one character is always replaced by the same character.

Shift Ciphers

Encryption where all letters in the alphabet are shifted by the same amount.

Substitution Ciphers

Ciphers of which the letters are randomly replaced.

Vernam Ciphers

A one-time pad cipher where each key should only be used once, requiring the key to be random and longer than the plaintext.

Computational Security

Ciphers that are crackable in theory, but not within a reasonable timeframe, relying on computational security.