Unit 3 data representation

AQA A-level Computer science

Natural Numbers

Whole numbers used for counting; an infinite set including 0.

Rational Numbers

Any value that can be expressed as a ratio or fraction, including all integer values.

Irrational Numbers

Numbers that cannot be expressed as a fraction and have an endless series of non-repeating digits (e.g., Pi).

Set of Integers

Represented by Z; includes all whole numbers and their negatives.

Set of Rational Numbers

Represented by Q; includes all numbers that can be expressed as a ratio of two integers.

Real Number (R)

Any rational or irrational number, but does not include imaginary numbers.

Ordinal Numbers

Describe the numerical position of objects (e.g., first in a race); used as pointers to a particular element in a sequence.

Number Base - Decimal

Our decimal system uses digits 0-9 and has a base of 10.

Number Base - Binary

Uses digits 0 and 1 and has a base of 2.

Number Base - Hexadecimal

Uses a base of 16.

Maximum values that can be represented using binary for n bits

(2^n) - 1

Hexadecimal System

A shorthand for binary, simpler to represent and less prone to errors.

Bit

A fundamental unit of information; either a single 1 or 0.

Nibble

A set of 4 bits.

Byte

A set of 8 bits.

Kibi (Ki)

2^10, 1024

Kilo (K)

10^3

Mebi (Mi)

2^20, 1048576

Mega (M)

10^6

Gibi (Gi)

2^30, 1073741824

Giga (G)

10^9

Tebi (Ti)

2^40, 1099511627776

Tera (T)

10^12

Pebi (Pi)

2^50

Peta (P)

10^15

Exbi (Ei)

2^60

Exa (E)

10^18

Zebi (Zi)

2^70

Zetta (Z)

10^21

Yobi (Yi)

2^80

Yotta (Y)

10^24

ASCII Code

Historically the standard code for representing characters; uses 7 bits.

Unicode

A 16-bit code that allows for 65536 different combinations representing alphabets from dozens of languages.

Parity Bit

An additional bit used to check that the other bits transmitted are likely to be correct.

Majority Voting

Requires each bit to be sent 3 times; computer goes with the majority if a bit value is flipped.

Checksum

A mathematical operation applied to a unit of data; checksum value is transmitted with the block.

Check Digit

Similar to a checksum; an additional digit added to a string of numbers to check for mistakes.

Overflow

When 8 bits are used and the result of a calculation is bigger than 255, requiring a ninth bit.

Two’s Complement

Flip all the digits and then add one.

Fixed Point Binary Numbers

A way to represent fractions in binary using a binary point to separate whole numbers from the fractional part.

Bitmap or Raster Image

Contains many pixels (picture elements) that make up the whole image.

Resolution

Expressed as the width in pixels * the height in pixels.

Resolution (pixels per inch)

Expressed as the number of pixels per inch or PPI; indicates the density of the pixels.

Color Depth

The number of bits that determine the number of color combinations a pixel can represent.

File Size (bitmapped image)

Resolution * color depth.

Meta Data

Data about data; includes details such as width in pixels, color depth, date and time taken.

Vector Graphics

Images made up of geometric shapes or objects; stores only necessary details to redraw the image.

Sound Waves

Naturally occurring in a continuous analogue form; converted to a discrete digital format for computers.

Sample Rate

The frequency with which you record the amplitude of the sound; affects the smoothness of playback.

Calculating Sound Sample Sizes

Number of samples per second * number of bits per sample * length of the sample in seconds.

Analogue Signal

A continuous signal which represents physical measurements.

Digital Signal

Discrete time signals generated by digital modulation.

Analogue to Digital Conversion

The process of converting analogue sound into digital recording, using an ADC.

Interpreting Frequency

Determined by the speed of oscillation or vibration of a wave; controls the pitch and is measured in hertz (Hz).

Nyquist's Theorem

Sample rate must be double the highest frequency in the original signal.

Musical Instrument Digital Interface (MIDI)

A technical standard that describes a protocol for connecting electronic musical instruments and computers.

Compression Algorithms

Reduces the storage needed for files on a disk; can be lossy or lossless.

Lossy Compression

Removes unnecessary information from the original file, resulting in loss of quality.

Lossless Compression

Retains all the information to replicate the file exactly.

Run Length Encoding (RLE)

Records the value of how many times a pixel has been repeated.

Dictionary Based Compression Techniques

Searches through the text to find suitable entries for its own dictionary and stores these words as a binary value.

Encryption

Transformation of data into a different form to prevent unauthorized access; plain text becomes cypher text.

The Caesar Cypher

Works by shifting the letters of the alphabet along by a given number of characters.

The Vernam Cypher

Uses one time pad ciphers which, if used properly, provide perfect security.