Number Systems and Binary Arithmetic
Representing and converting integers and real values in binary, denary and hexadecimal, then reasoning about range, precision and arithmetic effects.
How to study A-level Computer Science
Define the problem and representation, trace the state change, justify the algorithm or architecture, then test the result against requirements, evidence and constraints.
Core concepts
Concept 1
A positional number system gives each digit a value determined by its symbol and place.
Exam cue: State the bit width and signed representation before calculating range or decoding a pattern.
Concept 2
Unsigned, signed and floating-point representations trade range, precision and implementation complexity.
Exam cue: Show place values or repeated division rather than guessing a conversion.
Concept 3
Finite representations can overflow, underflow or introduce rounding error.
Exam cue: Check whether an arithmetic result is representable in the available bits.
Risk pitfalls and guardrails
Interpreting a bit pattern without knowing whether it is signed.
Guardrail: Do not substitute a memorised definition or generic advantage until you have identified the input, state, stakeholder and constraint in the task.
Assuming floating-point values represent every decimal exactly.
Guardrail: Do not substitute a memorised definition or generic advantage until you have identified the input, state, stakeholder and constraint in the task.
Dropping carry or sign information during binary arithmetic.
Guardrail: Do not substitute a memorised definition or generic advantage until you have identified the input, state, stakeholder and constraint in the task.
Memory anchors
Bit
A bit is a binary digit with value zero or one.
Hexadecimal
One hexadecimal digit represents four binary bits.
Two's Complement
Two's complement represents signed integers with one zero and straightforward binary addition.
Overflow
Overflow occurs when a result is outside the representable range.
Floating Point
Floating-point representation trades exactness for a wide range of magnitudes.
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
How many distinct bit patterns can be represented with 8 bits?
What is unsigned binary `101101` in denary?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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