Theory Topics & Mark Scheme Patterns

This lesson covers the key theory topics tested on AQA GCSE Computer Science Paper 2, with a focus on the specific methods, mark scheme expectations, and common errors for each topic. Understanding how AQA marks each topic will help you write answers that earn maximum marks.

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Data Representation: Binary, Hexadecimal, and Denary

Converting Between Number Systems

You must be able to convert fluently between binary (base 2), denary (base 10), and hexadecimal (base 16).

Binary to Denary

Use place values. An 8-bit binary number has the following columns:

128	64	32	16	8	4	2	1

Example: Convert 10110101 to denary.

128	64	32	16	8	4	2	1
1	0	1	1	0	1	0	1

128 + 32 + 16 + 4 + 1 = 181

Denary to Binary

Subtract the largest possible place value repeatedly.

Example: Convert 200 to binary.

• 200 - 128 = 72 → bit 7 = 1
• 72 - 64 = 8 → bit 6 = 1
• 8 < 32 → bit 5 = 0
• 8 < 16 → bit 4 = 0
• 8 - 8 = 0 → bit 3 = 1
• Remaining bits = 0

Answer: 11001000

Binary to Hexadecimal

Split the binary into nibbles (groups of 4 bits), then convert each nibble to hex.

Binary nibble	Hex digit
0000	0
0001	1
0010	2
0011	3
0100	4
0101	5
0110	6
0111	7
1000	8
1001	9
1010	A
1011	B
1100	C
1101	D
1110	E
1111	F

Example: Convert 10110101 to hexadecimal.

• Split: 1011 | 0101
• 1011 = B, 0101 = 5
• Answer: B5

Hexadecimal to Binary

Convert each hex digit to its 4-bit binary equivalent.

Example: Convert 3F to binary.

• 3 = 0011, F = 1111
• Answer: 00111111

Common Conversion Errors

Error	How to Avoid
Forgetting to pad nibbles to 4 bits	Always write full 4-bit groups: 3 → 0011, not 11
Mixing up hex digits A–F	A=10, B=11, C=12, D=13, E=14, F=15 — memorise this
Adding place values incorrectly	Write the calculation out step by step
Confusing binary with denary	Always label your answer with the base

Exam Tip: Always show your working for conversion questions. Even if your final answer is wrong, you can earn method marks for a correct process.

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Binary Arithmetic

Binary Addition

Follow the same rules as denary addition, but with only two digits (0 and 1):

Operation	Result
0 + 0	0
0 + 1	1
1 + 0	1
1 + 1	10 (write 0, carry 1)
1 + 1 + 1	11 (write 1, carry 1)

Example: Add 01101001 + 00110110

  01101001
+ 00110110
----------
  10011111

Working from right to left:

• 1+0=1, 0+1=1, 0+1=1, 1+0=1, 1+1=10 (write 0, carry 1), 1+1+1=11 (write 1, carry 1), 0+0+1=1, 0+0=0

Exam Tip: Write the carry digits above the calculation neatly. Examiners award marks for correct working, even if the final answer has an error.

Overflow

If binary addition produces a result that requires more bits than are available, an overflow error occurs. For example, adding two 8-bit numbers and getting a 9-bit result.

Example: 11111111 + 00000001 = 100000000 (9 bits — overflow in an 8-bit system)

Binary Shifts (Logical)

A logical shift moves all bits left or right by a specified number of positions.

Shift	Operation	Effect on Value
Left shift by 1	All bits move left, 0 fills the right	Multiplies by 2
Left shift by 2	All bits move left by 2 positions	Multiplies by 4
Right shift by 1	All bits move right, 0 fills the left	Integer divides by 2
Right shift by 2	All bits move right by 2 positions	Integer divides by 4

Example: 00011010 (26 in denary)

• Left shift by 1: 00110100 (52 — doubled)
• Right shift by 1: 00001101 (13 — halved)

Exam Tip: Bits shifted off the edge are lost. A left shift can cause data loss if significant bits fall off the left end.

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Character Encoding: ASCII and Unicode

ASCII (American Standard Code for Information Interchange)

• Uses 7 bits per character (128 characters total)
• Extended ASCII uses 8 bits (256 characters)
• Encodes standard English letters (A–Z, a–z), digits (0–9), punctuation, and control characters
• 'A' = 65, 'B' = 66, ..., 'Z' = 90
• 'a' = 97, 'b' = 98, ..., 'z' = 122
• '0' = 48, '1' = 49, ..., '9' = 57

Unicode

• Designed to represent every character in every language worldwide
• Can use 8, 16, or 32 bits per character
• Includes emojis, mathematical symbols, Chinese/Japanese/Korean characters, Arabic, Cyrillic, and many more
• The first 128 Unicode characters are identical to ASCII (backward compatible)
• Much larger character set but requires more storage space per character

Comparison Table

Feature	ASCII	Unicode
Bits per character	7 (or 8 extended)	8, 16, or 32
Total characters	128 (or 256)	Over 143,000
Languages supported	English only	All languages
Storage per character	1 byte	1–4 bytes
Compatibility	Subset of Unicode	Backward compatible with ASCII

Exam Tip: A common AQA question is "Explain why Unicode is needed instead of ASCII." The answer: ASCII can only represent 128/256 characters, which is insufficient for non-Latin scripts. Unicode supports characters from all world languages, making it essential for international communication and software localisation.

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Image Representation

How Images Are Stored

Digital images are made up of pixels (picture elements). Each pixel has a colour value stored as binary data.

Key terms:

Term	Definition
Pixel	The smallest addressable element of an image
Resolution	The number of pixels in the image (width × height)
Colour depth	The number of bits used to represent the colour of each pixel
Metadata	Additional data stored with the image (dimensions, colour depth, file type)

File Size Calculation

Formula:

File size (bits) = width (pixels) × height (pixels) × colour depth (bits per pixel)

To convert to bytes: divide by 8 To convert to kilobytes: divide by 1,024 To convert to megabytes: divide by 1,024 again

Example: An image is 800 × 600 pixels with 24-bit colour depth.

• File size = 800 × 600 × 24 = 11,520,000 bits
• = 11,520,000 ÷ 8 = 1,440,000 bytes
• = 1,440,000 ÷ 1,024 = 1,406.25 KB
• = 1,406.25 ÷ 1,024 ≈ 1.37 MB

Effect of Changing Image Properties

Change	Effect on Quality	Effect on File Size
Increase resolution	Image becomes sharper/more detailed	File size increases
Decrease resolution	Image becomes blockier/pixelated	File size decreases
Increase colour depth	More colours available, smoother gradients	File size increases
Decrease colour depth	Fewer colours, potential banding	File size decreases

Exam Tip: AQA frequently asks you to calculate the file size of an image AND explain how changing the resolution or colour depth affects both quality and file size. Practise these calculations until they are automatic.

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Sound Representation

How Sound Is Stored Digitally

Sound is an analogue signal that must be sampled (measured at regular intervals) and converted to digital data.

Key terms:

Term	Definition
Sample rate	The number of samples taken per second (measured in Hz)
Bit depth	The number of bits used to represent each sample
Duration	The length of the audio recording in seconds

File Size Calculation

Formula:

File size (bits) = sample rate (Hz) × bit depth (bits) × duration (seconds)

For stereo: multiply by 2 (two channels)

Example: A 30-second mono audio clip with a sample rate of 44,100 Hz and 16-bit depth.

• File size = 44,100 × 16 × 30 = 21,168,000 bits
• = 21,168,000 ÷ 8 = 2,646,000 bytes
• = 2,646,000 ÷ 1,024 ≈ 2,583.98 KB
• ≈ 2.52 MB

Effect of Changing Sound Properties

Change	Effect on Quality	Effect on File Size
Increase sample rate	More accurate representation of the sound wave	File size increases
Decrease sample rate	Loss of detail, sound may become distorted	File size decreases
Increase bit depth	Each sample is more precise, wider dynamic range	File size increases
Decrease bit depth	Loss of precision, quantisation noise	File size decreases

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Compression

Why Compress Data?

• Reduces file size for faster transmission over networks
• Saves storage space
• Reduces bandwidth usage

Lossy Compression

• Permanently removes some data to reduce file size
• Cannot restore the original file after compression
• Best for media files where small quality losses are acceptable (JPEG images, MP3 audio, MP4 video)
• Achieves much higher compression ratios than lossless
• Example: MP3 audio removes frequencies humans cannot easily hear

Lossless Compression

• Reduces file size without losing any data
• The original file can be perfectly reconstructed from the compressed version
• Best for text, code, data files, and situations where accuracy is essential (PNG images, FLAC audio, ZIP archives)
• Lower compression ratios than lossy
• Uses techniques like run-length encoding (RLE) and dictionary-based compression

Comparison Table

Feature	Lossy	Lossless
Data loss	Yes — some data permanently removed	No — all original data preserved
Compression ratio	High (files much smaller)	Lower (files moderately smaller)
Reversibility	Cannot restore original	Can restore original exactly
Best for	Photos, music, video	Text, code, medical images, archives
Examples	JPEG, MP3, MP4	PNG, FLAC, ZIP