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 — e.g. 8/1.

Irrational Numbers

Numbers that cannot be represented as a fraction — e.g. √2.

Real Numbers (R)

A number that a possible real-world 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.

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.

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.

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

The fundamental unit of information, which can either be 0 or 1. 2ⁿ values can be represented with n bits.

Bytes

A group of 8 bits.

Kilobyte

kB, 10³ bytes.

Megabyte

MB, 10⁶ bytes.

Gigabyte

GB, 10⁹ bytes.

Terabyte

TB, 10¹² bytes.

Kibibyte

KiB, 2¹⁰ bytes.

Mebibyte

MiB, 2²⁰ bytes.

Gibibyte

GiB, 2³⁰ bytes.

Tebibytes

Tib, 2⁴⁰ bytes.

Signed Binary

A binary item that can hold positive or negative values using two’s complement.

Unsigned Binary

A binary item that does not distinguish between positive and negative numbers. The minimum value for a unsigned binary value is 0, and the maximum value is 2ⁿ-1.

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 signed 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.

Fixed Point Binary Advantages

Points close to the MSB allow for good precision, points close to the LSB allow for good range.

Fixed Point Binary Disadvantages

Points close to the MSB produce a smaller range, points close to the LSB produce little precision.

Floating Point Binary

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.

Floating Point Binary Advantages

A greater range of numbers can be represented with a given number of bits. A large exponent with a small mantissa allows for a large range, a small exponent with a large mantissa allows for good precision.

Floating Point Binary Disadvantages

A large exponent with a small mantissa produces little precision, a small exponent with a large mantissa produces a small range.

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

Rounding Errors

Some numbers, such as 0.1₁₀ can only be approximately represented — thus some representations may be inaccurate.

Absolute Error

The difference between the actual number and the nearest representable value.

Relative Error

The absolute error as a percentage of the true value.

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.

Transmission Errors Causes

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.

Analogue Data

Continuous data that can be any float from 0 to 1.

Analogue Signals

A transmission of a set of analogue data structures, that varies with time, between computation processes.

Digital Data

Discrete data that can be 0 or 1.

Digital Signals

A transmission of a set of digital data structures, that varies with time, between computational processes.

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).

Colour Depth

The number of bits stored for each pixel.

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.

Metadata Examples

Width, height, colour depth.

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).

Nyquist 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).

Musical Instrument Digital Interface (MIDI)

A protocol for ADC audio transmission to a digital interface used for the majority of electronic musical instruments and computers.

Musical Instrument Digital Interface Advantages

Allows for easy manipulation of music without loss of quality, smaller in size than sampled audio files.

Musical Instrument Digital Interface Disadvantages

Cannot be used for storing speech, sometimes results in a less realistic sound.

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

Using an algorithm and a key to convert message data into a form that is not understandable without that key.

Caesar Cipher

A basic an insecure form of encryption, where characters are shifted by a consistent amount.

Caesar Shift Cipher

Letters are shifted by the same amount alphabetically, and the ‘shift’ becomes the key.

Caesar Substitution Cipher

The letters are randomly replaced.

Caesar Cipher Disadvantages

Can be easily cracked due to the frequency of occurrence.

Vernam Cipher

A mathematically unbreakable cipher, that is truly random sequence that is equal or longer in length than the plaintext and only ever used once.

Vernam Cipher Encryption

Aligning the plaintext and the key, converting each character to binary, applying a logical XOR operation, converting the result back into characters.

Computational Security Ciphers

Ciphers that are theoretically crackable, but not within a reasonable timeframe.

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.