Binary, Decimal and Hexadecimal
Representing unsigned values in positional number systems and converting accurately among binary, decimal and hexadecimal.
How to study for GCSE Computer Science
Move repeatedly between problem, algorithm, trace, code, test evidence and system explanation; use the exact language and assessment format required by your current board.
Core concepts
Concept 1
Positional notation weights each digit by a power of the base; binary uses base 2 and hexadecimal uses base 16.
Exam cue: Write place values before converting to reduce arithmetic mistakes.
Concept 2
One hexadecimal digit corresponds exactly to four binary bits, enabling direct grouping conversions.
Exam cue: Pad binary on the left when grouping into nibbles without changing its value.
Concept 3
A fixed number of bits gives a finite unsigned range, with maximum value one less than the next power of two.
Exam cue: State the bit width before deciding whether a value can be represented.
Risk pitfalls and guardrails
Reading a binary string as decimal digits.
Guardrail: Do not substitute one board's syntax, protocol list, language version or extension topic for the multi-board core; check the current specification and exam year.
Grouping binary from the left instead of from the least significant end.
Guardrail: Do not substitute one board's syntax, protocol list, language version or extension topic for the multi-board core; check the current specification and exam year.
Assuming the maximum unsigned 8-bit value is 256.
Guardrail: Do not substitute one board's syntax, protocol list, language version or extension topic for the multi-board core; check the current specification and exam year.
Memory anchors
Bit
A binary digit with value 0 or 1.
Nibble
A group of four bits.
Byte
A group of eight bits.
Hexadecimal
Base-16 notation using digits 0-9 and symbols A-F.
Most significant bit
The bit with the greatest positional value in a representation.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
What is the denary value of unsigned binary `10110`?
What is the denary value of unsigned binary `111111`?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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