Place Values
Multiply each digit by its place value and sum the results.
Binary
2⁷ 2⁶ 2⁵ 2⁴ 2³ 2² 2¹ 2⁰ Hexadecimal
16³ 16² 16¹ 16⁰ Cambridge IGCSE 0478 / 0984
💻 IGCSE Computer Science Formula Sheet 2025
Binary arithmetic, logic gates, storage calculations, network speeds and algorithmic metrics summarised for fast revision.
Binary & Hex Logic Gates Performance Networking
Translate Theory into Accurate CS Calculations
Cambridge Computer Science questions often combine binary maths with hardware and networking principles. Use this sheet to keep all the required conversions, formulas and data size conversions in a single, exam-friendly format.
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Binary ↔ decimal ↔ hexadecimal conversions
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Logic gate outputs with Boolean notation
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CPU performance & sound/image file calculations
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Network bandwidth, latency & transmission time
Number Bases & Data Representation
Show working clearly when converting between bases to secure method marks.
Binary to Decimal
Position starts from 0 at the rightmost bit.
Decimal = Σ (bit × 2^position) Decimal to Binary (Division Method)
Repeatedly divide by 2, record remainders, read in reverse order. Decimal to Hexadecimal
Repeatedly divide by 16, convert remainders (10–15 → A–F), read in reverse order. Binary to Hexadecimal
Group binary digits into sets of four (from the right) and convert each nibble to hex. Two’s Complement Negative Representation
Remember the most significant bit indicates the sign in 8-bit representation.
Invert bits (1's complement), then add 1 to LSB. Binary Addition Rules
Check for overflow if carry extends beyond the bit-length.
0 + 0 = 0 carry 0
0 + 1 = 1 carry 0
1 + 1 = 0 carry 1
1 + 1 + 1 = 1 carry 1
Data Storage & Media Calculations
Storage Units
1 nibble = 4 bits 1 byte = 8 bits 1 kilobyte (KB) = 1024 bytes 1 megabyte (MB) = 1024 KB 1 gigabyte (GB) = 1024 MB Text File Size (ASCII/Unicode)
For ASCII use 7/8 bits; for UTF-16 use 16 bits.
File size (bits) = Number of characters × Bits per character Image File Size (Uncompressed Bitmap)
Colour depth = number of bits per pixel.
Image Size
File size (bits) = Width × Height × Colour depth File size (bytes)
Bytes = (Width × Height × Colour depth) / 8 Sound File Size
Uncompressed audio
File size (bits) = Sample rate × Bit depth × Duration (seconds) × Number of channels Video File Size (simplified)
Frame size = width × height × colour depth. Apply compression ratio if specified.
File size (bits) ≈ Frame size (bits) × Frame rate × Duration Logic Gates & Boolean Algebra
Gate Output Rules
NOT
¬A → inverts the input AND
A · B → output 1 only if A = 1 AND B = 1 OR
A + B → output 1 if A = 1 OR B = 1 NAND
¬(A · B) NOR
¬(A + B) XOR
A ⊕ B → output 1 if inputs are different De Morgan’s Laws
Useful for simplifying Boolean expressions.
¬(A · B) = ¬A + ¬B ¬(A + B) = ¬A · ¬B Truth Table Construction
For n inputs, total rows = 2ⁿ. List binary combinations systematically.
Half Adder Boolean
Full adder uses XOR for sum and includes carry-in.
Sum
S = A ⊕ B Carry
C = A · B CPU Performance & Networking
CPU Performance Metrics
CPI = cycles per instruction. Mention factors like cache and pipelining in explanations.
Clock Time per Cycle
Time per cycle = 1 / Clock speed Execution Time
Execution time = Number of cycles × Time per cycle Power of parallel cores
Total throughput ≈ Clock speed × Number of cores × CPI adjustment Data Transfer & Bandwidth
Bandwidth (bps)
Bandwidth = Data transferred / Time Transmission Time
Transmission time = File size (bits) / Transmission rate (bits per second) Latency & Propagation Delay
Latency = Propagation delay + Transmission delay + Processing delay Bit Rate vs Baud Rate
For binary signalling, bit rate equals baud rate.
Bit rate = Baud rate × Bits per signal change Checksum / Parity Concepts
Even parity: total number of 1s must be even; odd parity: total number of 1s must be odd. Checksum values depend on protocol rules.
Algorithmic Reasoning & Flowcharts
Average / Sum Calculations in Pseudocode
Always initialise accumulators (total ← 0, count ← 0) before loops.
Average
average ← total / count Running total
total ← total + nextValue Binary Search Iteration Count
n = number of sorted items.
Maximum comparisons ≈ ⌈log₂(n)⌉ Complexity Notation Reminder
Know Big-O for common algorithms: linear search O(n), binary search O(log n), bubble sort O(n²) average/worst.
Validation vs Verification
Validation checks data reasonableness (range, length); verification ensures data copied accurately (double entry, visual check).
How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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Write Out Conversions
Lay out each step for binary ↔ decimal ↔ hexadecimal conversions so examiners can award method marks even with minor errors.
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Pair Formulas with Concepts
After each calculation, explain what it means for hardware, networking or algorithm efficiency to capture explanation marks.
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Practice Timed Binary Arithmetic
Use a one-minute drill to add and subtract binary numbers daily so overflow and carry rules become second nature.
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Build Reference Tables
Create your own tables for ASCII codes, hex digits and logic gate outputs to reduce memorisation stress on exam day.
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Based on Cambridge Assessment International Education IGCSE Computer Science (0478/0984) syllabus for 2025 examination series.
Always reference units (bits, bytes, Hz, seconds) in final answers and convert file sizes before dividing by transmission rates.