3.5 Data Representation Flashcards
Natural Numbers
Numbers used in counting. Any integer greater than or equal to 0.
Rational Numbers
Numbers which can be expressed as fractions (includes x/1)
Irrational Numbers
Numbers which cannot be expressed as fractions.
Real Numbers
The set which contains natural, rational and irrational numbers.
Integer numbers
All positive and negative whole numbers
Ordinal Numbers
Numbers which describe the positions of things (e.g. first
Hexadecimal
Base 16
Why Hex?
Easier to represent longer numbers for human interpretation.
Binary Prefixes
Kibi, mebi, gibi, etc.
Decimal Prefixes
Kilo, mega, giga, etc.
Unsigned Binary
Binary that represents positive numbers only
Signed Binary
A binary number system that can represent both positive and negative numbers e.g. Two’s Complement Form
Two’s Complement
Most significant bit is negative. E.g. for an 8 bit string
Converting between decimal and two’s complement
Make the decimal positive (e.g. -9 -> 9), convert to binary, flip the bits and add 1.
Converting between two’s complement and decimal
Flip the bits, add 1 then convert.
Fixed Point Binary
Allows you to represent fractional numbers in binary.
Character set
Set of alphanumeric characters and symbols which can be represented on a computer system.
Original ASCII
Character set for English characters and numbers which could only represent 128 characters.
Extended ASCII
Character set which uses 8 bits and stores a few more symbols than ASCII
Unicode
Character set which uses 16 or 32 bits to support many different characters e.g. Chinese and Emojis.
Parity Bits
An additional bit sent along with the rest of the data to ensure it is transmitted correctly.
Majority Voting
Each bit is sent an odd number of times (>1). The bit that appears the most out of the set is used.
Checksums
Mathematical algorithms applied to each packet of data. If the result of the maths is equal on both ends, the data has been transmitted successfully.
Check Digits
Additional digit on the end of a string of numbers. E.g. 13th digit of an ISBN.
Resolution (image)
Width pixels x height pixels. Can also be expressed as PPI.
Colour Depth
Bits required per pixel. Given as 2^n
PPI
Pixels per inch. Describes the density of pixels.
Analog to digital converter for sound
Samples amplitude of analogue wave at sample rate times per second.
Sample rate
Number of samples taken per second. Measured in Hz.
File size of sound
Sample rate x bit depth x duration in seconds
Bit depth
Number of bits per sample
Nyquist Theorem
Sample rate must be at least double the highest frequency of an original sound for an accurate recording.
Continuous data
Data which can be of any numerical value.
Discrete data
Data which can only take certain values.
MIDI
Allow for electronic musical instruments and computers to communicate. Files are instructions for replication
MIDI Contoller
Carry event messages (e.g. pitch)
Why compress data?
To save space on storage media or take up less bandwidth during transmission.
Lossy compression
All unnecessary info is removed. Smaller file sizes.
Lossless compression
All unnecessary info is removed but data to recreate is kept.
Run Length Encoding
Consecutive identical data is stored as how many times it occurs, rather than itself on each occurance.
Dictionary based compression
Repeating patterns are assigned values and placed into a dictionary and sent along with the main files.
Encryption
Prevents unauthorised people from reading data.
Encryption key
Information needed to decipher the encrypted data.
Caesar cipher
Shift each letter by x number of characters where x is the key.
Vernam Cipher
Uses a one time pad XORd with its corresponding character in the plaintext. Perfect security as OTP must be destroyed after use.
Image size
Dimensions x Colour Depth
