AQA A-Level Computer Science Paper 2 (Python)

Natural Numbers (N)

Positive Integers that are used for counting; 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 a possible real-life quantity and is used for measurement

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 X₂ such as 11₂ 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 X₁₀ such as 11₁₀ 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 X₁₆ such as 11₁₆ representing 17.

Hexadecimal Representation of Numbers

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

Signed Binary

A binary item that can hold positive or negative values

Unsigned Binary

A binary item that does not distinguish between positive and negative numbers

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). Work out the positive number, switch the 1s and 0s, and add 1.

Two's Complement Range

127₁₀ to -128₁₀

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 2ⁿ where m is the mantissa, and n is the exponent. Convert the number into binary, with the MSB as a sign bit. The amount that the decimal point moves is 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

Absolute Error

The difference between a measured value and the true value

Relative Error

The absolute error as a percentage of the true value

Analogue Data

Continuous data that can be any float from 0 to 1

Digital Data

Discrete data that can be 0 or 1

Analogue to Digital Conversion (ADC)

Digitisation uses sampling and quantisation to store and process analogue data

Sampling

Taking frequent measurements of an analogue signal at uniform time intervals

Quantisation

Mapping the measured analogue samples to a series of discrete digital values

Digital to Analogue Conversion (DAC)

Takes a series of binary numbers and produces a continuous analogue signal

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