Binary to Decimal
Sum each bit multiplied by 2 raised to its position (starting from 0 on the right).
Decimal = ฮฃ (bit ร 2^position) AQA GCSE 2025
๐ป AQA GCSE Computer Science Formula Sheet
Essential formulas for binary conversions, logic gates, storage calculations, networking, and CPU performance aligned to AQA GCSE Computer Science (8525) specification.
Binary & Hex Logic Gates Storage Networking
Master GCSE Computer Science
This formula sheet covers fundamental computer science relationships from the AQA GCSE Computer Science specification, helping you solve problems involving binary arithmetic, data storage, and system performance.
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Binary conversions
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Logic gate rules
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Storage calculations
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Network formulas
Number Bases & Conversions
Converting between binary, decimal, and hexadecimal number systems.
Decimal to Binary
Repeatedly divide by 2, record remainders, read in reverse order.
Continue until quotient is 0.
Binary to Hexadecimal
Group binary digits into sets of four (from right), convert each group to hex.
Each hex digit represents 4 bits (a nibble).
Hexadecimal to Decimal
Multiply each hex digit by 16 raised to its position, sum results.
Decimal = ฮฃ (hex_digit ร 16^position) Topic Focus
Number System Conversions
- Always show your working when converting between number bases to secure method marks.
- Binary uses base 2 (digits 0-1); hexadecimal uses base 16 (digits 0-9, A-F).
- Group binary digits in sets of 4 for hex conversion (pad with zeros if needed).
Data Storage Calculations
Calculating file sizes and storage requirements for different data types.
Storage Units
Binary storage units (powers of 2).
1 byte = 8 bits 1 KB = 1024 bytes 1 MB = 1024 KB 1 GB = 1024 MB Text File Size
Number of characters ร bits per character.
ASCII uses 7-8 bits; Unicode uses 16+ bits per character.
File size (bits) = Characters ร Bits per character Image File Size
Uncompressed bitmap image size.
File size (bits) = Width ร Height ร Colour depth Sound File Size
Uncompressed audio file size.
File size (bits) = Sample rate ร Bit depth ร Duration ร Channels Topic Focus
File Size Calculations
- Always check units: bits vs bytes (divide by 8 to convert bits to bytes).
- Colour depth = number of bits per pixel (e.g., 24-bit = 3 bytes per pixel).
- For compressed files, multiply by compression ratio if given.
Logic Gates & Boolean Algebra
Understanding logic gate operations and Boolean expressions.
Basic Logic Gates
Standard logic gate operations.
AND
A ยท B (output 1 only if both inputs are 1) OR
A + B (output 1 if either input is 1) NOT
ยฌA (inverts the input) XOR
A โ B (output 1 if inputs differ) Topic Focus
Logic Gate Operations
- AND gate: both inputs must be 1 for output to be 1.
- OR gate: at least one input must be 1 for output to be 1.
- NOT gate: inverts the input (1 becomes 0, 0 becomes 1).
CPU Performance & Networking
Calculations for processor performance and network transmission.
CPU Performance
Instructions per second calculation.
MIPS = (Clock speed in Hz) / (Average cycles per instruction) Network Transmission Time
Time to transmit data over a network.
Time = File size (bits) / Bandwidth (bits per second) Topic Focus
Performance Calculations
- Higher clock speed and lower cycles per instruction improve CPU performance.
- Network transmission time depends on file size and available bandwidth.
- Always use consistent units (bits or bytes) in calculations.
How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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Show Your Working
Always show step-by-step conversions between number bases. This helps secure method marks even if the final answer is incorrect.
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Check Units
Pay attention to units: bits vs bytes, and storage units (KB, MB, GB) which use powers of 1024, not 1000.
Excel in AQA GCSE Computer Science
Master computer science calculations with expert GCSE tutors who help you understand computational concepts and apply formulas confidently.
Formulas align with AQA GCSE Computer Science specification (8525) for UK students.
Always show your working, check units carefully, and verify conversions are correct.