Data Representation AQA

Natural number, N

Natural number, N

positive integers including 0

Integer, Z

positive and negative whole numbers

Rational number, Q

fractions and decimal numbers

Real number, R

all numbers with real world quantities

Irrational numbers

non integers that cannot be written as a fraction, eg. pi and surds

Binary

1 or 0 used for each digit, represented by computers with high and low current

Hexadecimal

16 different characters for each digit, 0-9 and A-F, most compact number base

Bit

the fundemental unit of infomation

Byte

a group of 8 bits

Binary byte prefixes

kibi, mebi, gibi, tebi

Decimal byte prefixes

kilo, mega, giga, tera

Unsigned binary

only represents positive numbers

Signed binary

first byte makes the number negative or positive, the range is 2^n - 1 (n bits)

Subtracting using two’s complement

to subtract, add the negative of the second number

Fixed point binary

a specified number of bits are placed before a binary point and the remaining bits fall behind it

Floating point binary

similar to scientific notation, always uses two’s complement, mantissa holds the number, exponent holds the shift, convert exponent to decimal, then move binary point by the decimal exponent, requires normalisation so it starts with 01 for positive and 10 for negative

Absolute errors

Absolute is the amount by which the value is inaccurate from the original,

Relative errors

relative is a measure of uncertainty, the absolute error over the original value

Fixed point vs Floating point

Floating allows a greater range of numbers, a larger exponent gives more range, a larger mantissa gives more precision

Underflow

occurs when very small numbers don’t have enough bits to be represented

Overflow

occurs when the number is too large to be represented

ASCII (American standard code for information interchange)

uses 7 bits to represent 128 characters, not as good as Unicode as unable to represent languages with different alphabets

Unicode

uses anything from 8 to 48 bits per character, represents a much wider ranges of characters than ASCII

Parity bit

a single bit added to a transmission to check for errors, even parity makes sure the number of 1s is even, odd parity makes sure the number of 1s is odd, when received the value of the parity bit is checked to the type to error check

Majority voting

each bit of data is transmitted multiple times, when received the most commonly occurring value is taken as correct, primary disadvantage is the volume of data being transmitted increases, increasing the time taken to transmit

Checksums

an algorithm is applied to the data, the value is the appended to the original data before transmission, once received the same algorithm is applied to ensure the checksum matches

Check digit

like a checksum but limited to 1 digit which reduces the number of algorithm available to use and reduces the variety of detectable errors

Analogue data and conversion

continuous with no limits to values, sensors output an analogue signal which is converted to a digital bit pattern by an ADC, works by taking readings at regular intervals in a process called sampling

Digital data and conversion

discrete and can only take particular values, a DAC is used to read a digital bit pattern representing an analogue signal and outputs an analogue electrical current which can be output by various devices like speakers (for sound)

Bitmap graphics

an image is made of pixels (picture elements) each assigned a binary value which determines the colour, resolution is number of pixels in image, number of bits assigned to a pixel is colour/ bit depth, storage required is resolution (num of pixels) x colour/bit depth

Vector graphics

uses geometric objects to represent images, properties like fill colour, fill styles and dimensions are stored in a list

Bitmap vs Vector

Vector use shapes so can be scaled without losing quality and are suited to simple images like logos, bitmap suits photography and takes more storage space for each pixel

Sound

number of bits in a sample is sample resolution, higher resolution means higher quality and file size, duration x sample rate (Hz) x sample res = size of sound file, sampling rate must be at least twice the frequency to be accurately represented

MIDI (Musical instrument digital interface)

stores sound as a series of event messages representing an event in a music piece, these can contain note duration, instrument, volume, pitch and sustaination, allows easy manipulation of music without quality loss, often smaller in size than sampled audio and are lossless, however normally less realistic sound and can’t store speech

Lossy compression

when information is lost in the process of reducing a file size, normally through reducing the resolution

Lossless compression

where there is no loss of information when reducing a file size

RLE (Run length encoding)

reduces file size by removing repeated information and replacing with an repetition number

Dictionary based compression

a dictionary containing repeated data is added to the file which adds to the size, can represent repeating patterns unlike RLE which only recognises repeating digits