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All sections of the AQA A Level specification except 4.7.4, 4.8, & 4.11. Will update as these are done in class. Good luck revising :)
Natural Numbers (N)
Positive Integers; N = {0, 1, 2, 3, ...}
Integer Numbers (Z)
Whole numbers; Z = {..., -1, 0, 1, ...}
Rational Numbers (Q)
Numbers that can be represented as a fraction (all integers are rational)
Irrational Numbers
Numbers that cannot be represented as a fraction
Real Numbers (R)
A number that exists (so not a conceptual number like Pi)
Ordinal Numbers
The positions used in lists (1, 2, 3, ...)
Base
The number of symbols used to construct values (also referred to as a subscript)
Base 2 (Binary)
A number system that uses 2 symbols, 0 & 1. Numbers in base 2 are written as X(v2) such as 11(v2) representing 3.
Binary Representation of Numbers
Uses 2^x to represent numbers, with x increasing by one every place, starting from the rightmost place. (So 1, 2, 4, 8, 16, 32, 64, 128)
Base 10 (Decimal)
A number system that uses 10 symbols, 0-9. Numbers in base 10 are written as X(v10) such as 11(v10) representing 11.
Decimal Representation of Numbers
Uses 10^x to represent numbers, with x increasing by one every place, starting from the rightmost place. (So 1, 10, 100)
Base 16 (Hexadecimal)
A number system that uses 16 symbols, 0-9 & A-F. Numbers in base 16 are written as X(v16) such as 11(v16) representing 17.
Hexadecimal Representation of Numbers
The Hexadecimal system uses 16^x to represent numbers, with x increasing by one every place, starting from the rightmost place. (So 1, 16, 256)
Hexadecimal Advantages
Easier to read and than binary, and easily converted into both denary and binary.
Decimal to Binary Conversion
From left to right in the place value table, subtract the place value from the decimal number where possible.
Decimal to Hex Conversion
Divide the decimal number by 16, and add the remainder.
Significance of 16
16 is 2^4, meaning that base 16 numbers can be translated from 4 consecutive bits of a binary value. This makes it simple to translate binary numbers into hexadecimal values and back again.
Bits
Each individual digit in a binary digit is referred to as a bit, from the term binary digit
Bytes
A collection of 8 bits
Kilobyte
KB, 10^3 bytes
Megabyte
MB, 10^6 bytes
Gigabyte
GB, 10^9 bytes
Terabyte
TB, 10^12 bytes
Kibibyte
KiB, 2^10 bytes
Mebibyte
MiB, 2^20 bytes
Gibibyte
GiB, 2^30 bytes
Tebibytes
Tib, 2^40 bytes
ASCII Code
In 1963, the American Standard Code for Information Interchange, was established to encode symbols found in the English alphabet. Important ASCII values: A = 65, a = 97
Unicode
Introduced to standardise the encoding of characters from all languages
Transmission errors
When data is transmitted, it doesn't always arrive in the same format that it was sent. These errors cause bits to flip from 1s to 0s and vice versa.
What causes Transmission errors?
Electrical interference, power surges, synchronisation issues, broken cables and connectors
Parity Bits
When sending a byte of data, one bit is used as a parity bit. This bit is set to a 1 or 0 to make the total numbers of 1s or 0s in the byte odd or even depending on the machine. If the wrong number of bits are 'on', an error has occurred.
Majority Voting
Each bit of a message is sent three times- if a bit value is flipped erroneously, the recipient computer uses the majority rule and assumes that two bits that have not changed were therefore correct.
Check Digits
An additional digit at the end of a string of data, designed to check for mistakes in input or transmission. The first 12 digits make up the data, and the 13th is calculated by an algorithm based on the other digits
Modulus 10
Add all the numbers, find the remainder when divided by 10, subtract remainder from 10. Used in check digits
Check Sums
A total sum of all bytes is calculated with an algorithm and sent with the data. When received, it is recalculated and compared to determine if any transmission errors have occurred
Binary Addition: 0 + 0 =
0
Binary Addition: 0 + 1 =
1
Binary Addition: 1 + 1 =
10
Binary Addition: 1 + 1 + 1 =
11
Overflow Error
When the result of an operation is too large for the number of bits the computer works with
Underflow Error
When the result of an operation is too small for the number of bits the computer works with
Binary Multiplication: 0 * 0 =
0
Binary Multiplication: 0 * 1 =
0
Binary Multiplication: 1 * 1 =
1
Two's Complement
A way of showing negatives in binary. The MSB is always 1 when a binary number is negative (a sign bit). After writing the positive version, the complement can be written by starting at the LSB, all bits until and including the first 1 stay the same. From there to the MSB, the numbers are reversed.
Two's Complement Range
127(v10) to -128(v10)
Binary Subtraction
Using two's complement of the second number allows for addition instead
Binary Fractions
Bits on the right after a notational point are fractional
Fixed-Point Binary
Uses a specified number of bits where the placement of the binary point is fixed
Floating Point Numbers
Held in the formant m x 10n where m is the mantissa, and n is the exponent. The MSB is a sign bit for the mantissa and the exponent
Normalisation
The process of moving the binary point of a floating-point number to provide the maximum level of precision for a given number of bits, by ensuring the first digit after a binary point is a significant digit
Relative Error
Calculated as percentage
Analogue Data
Continuous data that can be any float from 0 to 1
Digital Data
Discrete data that can be 0 or 1
Resolution
The number of pixels used the make up a bitmap (width x height)
Bit Depth
The amount of bits used to store information (colour, audio), calculated with 2^bits
Image File Size
Pixels * Bit Depth
Metadata
Data about data
Vector Images
Made up of geometric shapes rather than manipulating individual pixels. The properties of each shape are stored and retrieved in order to mathematically redraw the shape to display it.
Sound File Size
Sample rate * resolution * length (seconds)
Nyguist Theorem
Because sound is made up of many components at different frequencies, samples must be twice the highest frequency in order to replicate the original soundwave (fs > 2fmax)
Lossy
Non-essential data is permanently removed
Lossy Qualities
Reduces quality, used for images and sounds
Lossless Compression
Patterns in the data are spotted and summarised in a shorter format without permanently removing any information
Lossless Qualities
Does not reduce quality, used for text files and code
Run Length Encoding (RLE)
A basic method of compression that summarises consecutive patterns of the same data
Dictionary Compression
Spots regularly occurring data and stores it separately in a dictionary
Encryption
A way of making data unintelligible if the recipient doesn't have the means to decrypt it
Caesar Cipher
A basic an insecure form of encryption, where characters are shifted by a consistent amount
Vernam Cipher
An unbreakable cipher, that is truly random sequence that is equal or longer in length than the plaintext and only ever used once
Brute Force
Attempts to apply every possible key to decrypt ciphertext until it works
Algorithmic Security
Ciphers are based on computational security, with keys determined by an algorithm
Hardware
The physical components of the computer
Hardware Examples
Motherboards, hard drives, RAM
External Hardware
Peripherals that can be added or removed from a computer
External Hardware Examples
Monitors, keyboards, mice
Software
Programs which run on the hardware
System Software
Software required to run and manage the computer's hardware and application programs
System Software Examples
Allocates jobs to the processor, peripheral management, software installation
Operating System (OS)
A middleman for communication between the computer's hardware and software
Operating System Examples
Windows, Mac OS, Linux, Android
Operating System Tasks
Resource management, provision of a UI
Utility Software
Designed to analyse, configure, optimise, or maintain a computer system. Some perform additional common tasks needed by most or all users.
Utility Software Examples
Defragmentation, installation of software, virus checkers, automatic backup
Libraries
A collection of pre-compiled routines that can be used by other programs
Libraries Examples
Random, time, tkinter
Translators
Translates code from high level languages into machine code
Translator Examples
Assemblers, Compilers, Interpreters
Application Software
Allows the user to complete tasks
Application Software Examples
Word Processors, image editors, internet browsers
General Purpose Software
Software that can be used for a range of generic tasks
General Purpose Software Examples
Word processors, graphics packages, spreadsheet software
Special Purpose Software
Software that performs tasks for a single, specific job
Special Purpose Software Examples
Payroll software, Media players, Calendar programs
Off-the-shelf Software
Readily available software that is low cost and well tested
Bespoke Software
More expensive software created to fulfil exact specifications
Memory Management
Allocates memory to each process
Processor Scheduling
Controls which programs can send data to the processor, and queues instructions to create multi-tasking
The Schedular
Ensures that processor time is used as efficiently as possible
