AQA A-Level Computer Science Paper 2

Natural number

A non-negative whole number: 0, 1, 2, 3, …

Natural numbers symbol

ℕ

Integer

A whole number with no fractional part, including negative numbers and zero.

Integers symbol

ℤ

Rational number

A number that can be written exactly as a ratio of two integers.

Rational numbers symbol

ℚ

Irrational number

A number that cannot be written exactly as a ratio of two integers.

Real number

A number with no imaginary part; includes rational and irrational numbers.

Real numbers symbol

ℝ

Ordinal number

A natural number used to describe position or order.

Natural numbers usually used for

Counting quantities.

Real numbers usually used for

Measurement.

Number base

The number of different digits/symbols used in a number system.

Binary

A base 2 number system using only 0 and 1.

Decimal/denary

A base 10 number system using digits 0 to 9.

Hexadecimal

A base 16 number system using 0 to 9 and A to F.

Why is hexadecimal used as shorthand for binary?

One hexadecimal digit represents exactly four binary bits, making long binary values shorter and easier to read.

How do you convert binary directly to hexadecimal?

Group the binary digits into groups of four from the right, then convert each group to one hexadecimal digit.

Bit

A binary digit; the smallest unit of information, either 0 or 1.

Byte

A group of 8 bits.

Nibble/nybble

A group of 4 bits, equal to half a byte.

What does lowercase b normally mean in storage units?

Bits.

What does uppercase B normally mean in storage units?

Bytes.

Number of values from n bits

2^n different values.

Binary prefix

A unit prefix based on powers of 2, such as Ki, Mi, Gi and Ti.

Decimal prefix

A unit prefix based on powers of 10, such as k, M, G and T.

1 KiB

2^10 bytes = 1024 bytes.

1 MiB

2^20 bytes.

1 GiB

2^30 bytes.

1 TiB

2^40 bytes.

1 kB

10^3 bytes = 1000 bytes.

1 MB

10^6 bytes.

1 GB

10^9 bytes.

1 TB

10^12 bytes.

Unsigned binary

A binary representation that only represents non-negative numbers.

Range of an n-bit unsigned binary number

Minimum 0, maximum 2^n - 1.

Signed binary

A binary representation that can represent both positive and negative numbers.

Two’s complement

A signed binary system where negative values are represented using the most significant bit as a negative place value.

How do you find the negative of a binary number in two’s complement?

Invert all bits and add 1.

Range of n-bit two’s complement

-2^(n-1) to 2^(n-1) - 1.

Leading 1 in two’s complement

The number is negative.

Leading 0 in two’s complement

The number is non-negative.

Fixed point representation

A number representation where the position of the radix point is fixed.

Floating point representation

A number representation using a mantissa and exponent so the radix point can move.

Mantissa in floating point

The part that stores the significant digits of the number.

Exponent in floating point

The part that stores how far the radix point is moved.

Normalisation in floating point

Adjusting the mantissa and exponent so the number is represented in a standard, efficient form.

Why is floating point useful?

It can represent a wider range of very large and very small numbers than fixed point using the same number of bits.

Why can fixed point be better than floating point?

It can give greater precision within a smaller fixed range.

Overflow

An error when a number is too large to be represented using the allocated bits.

Underflow

An error when a number is too small/close to zero to be represented using the allocated bits.

Rounding error

An error caused when a value cannot be stored exactly and must be approximated.

Absolute error

The difference between the exact value and the stored/rounded value.

Relative error

The absolute error compared with the exact value, usually expressed as a percentage.

Character code

A binary code used to represent a character from a character set.

Why is character code for “7” different from binary value 7?

Character “7” is stored as a character code; value 7 is stored as a numeric binary value.

ASCII

A character coding system originally using 7 bits to represent 128 characters.

Unicode

A character coding system designed to represent characters from many languages and symbol sets.

Why was Unicode introduced?

ASCII could not represent enough characters for worldwide languages and symbols.

Parity bit

An extra bit added so the number of 1s is even or odd, allowing error detection.

Even parity

The parity bit is chosen so the total number of 1s is even.

Odd parity

The parity bit is chosen so the total number of 1s is odd.

Majority voting

Each bit is sent multiple times and the receiver chooses the value that appears most often.

Checksum

A value calculated from transmitted data and sent with it so the receiver can detect errors.

Check digit

An extra digit calculated from other digits in a code to detect entry or transmission errors.

Bitmap image

An image stored as a grid of pixels, with each pixel represented by a binary colour value.

Pixel

The smallest addressable element of a bitmap image.

Colour depth

The number of bits used to represent the colour of each pixel.

How many colours can n bits per pixel represent?

2^n colours.

Bitmap image size formula

width × height × colour depth, in bits.

Image resolution

The number of pixels in an image, often width × height.

Metadata in an image file

Data about the image, such as width, height, colour depth or file type.

Vector graphic

An image represented using objects/shapes and their properties rather than individual pixels.

Why can vector graphics use less storage than bitmaps?

They store descriptions of shapes, not every individual pixel.

One advantage of vector graphics over bitmaps

They can be scaled without pixelation/loss of quality.

One disadvantage of vector graphics

They are less suitable for complex, detailed photographs.

Analogue data

Data that varies continuously over a range of values.

Digital data

Data represented using discrete separate values, usually binary.

Analogue signal

A continuously varying signal.

Digital signal

A signal with discrete levels, commonly representing 0s and 1s.

ADC

Converts an analogue signal into digital values by sampling and quantising it.

DAC

Converts digital values into an analogue signal.

Why are ADCs used with analogue sensors?

Sensors often produce analogue voltages that must be converted into digital data for the computer.

Sampling rate

The number of samples taken per second.

Sample resolution

The number of bits used to store each sample.

Sound file size formula

sample rate × sample resolution × duration × channels, in bits.

Nyquist rule for sampling

The sampling rate should be at least twice the highest frequency in the sound.

What happens if sampling rate is too low?

The sound may not be recreated accurately; high frequencies can be lost or distorted.

Compression

Reducing the number of bits needed to store or transmit data.

Lossless compression

Compression where the original data can be perfectly reconstructed.

Lossy compression

Compression where some data is permanently removed, so the original cannot be perfectly reconstructed.

Run-length encoding (RLE)

A lossless method that stores repeated runs as a value and the number of times it occurs.

When is RLE effective?

When the data contains long repeated runs of the same value.

When is RLE ineffective?

When values change frequently and there are few long runs.

Dictionary-based compression

A lossless method that stores repeated patterns once in a dictionary and replaces occurrences with references.

Why may dictionary compression be poor for small text?

The dictionary overhead may be too large compared with the amount saved.

JSON

A lightweight text format for storing or transmitting structured data as attribute-value pairs.

Why might JSON be chosen over XML?

It is usually shorter, easier to parse, and less verbose.

XML

A text-based markup format that uses tags to structure data.

Hardware

The physical components of a computer system.