C09 · Topic 2.1 · 40 minutes · DAT-1.A, DAT-1.B, DAT-1.C
Bits and representations
By the end you can:
- Explain why a bit pattern needs a convention.
- Distinguish discrete data from continuous phenomena.
- Describe sampling and finite precision.
Start here; no earlier topic is required.
- Bit
- A binary digit,0 or 1.
- Sampling
- Taking measurements of a continuous quantity at selected times.
Understand
Computers represent information using bits. A sequence of bits can encode a number, text, colour or part of a sound when a convention supplies its meaning. Reading the same unchanged pattern under a different convention can produce a different valid interpretation.
A continuous phenomenon such as changing temperature must be sampled and represented with finite precision. Changes between sample times can be missed, and a stored measurement may be rounded. More frequent samples or finer precision can improve an approximation while increasing storage; exact copying does not recover information never recorded.
Worked example
A fictional sensor samples once an hour and rounds to the nearest whole degree. Readings 19.4,21.6,22.1 become 19,22,22.
- The 21.6 reading changes by+0.4 degrees when rounded to 22.
- A brief 25-degree spike between two hourly samples is absent from this record.
- The stored pattern 10110 means 22 degrees only under the documented unsigned-whole-degree convention.
Explore each concept
Choose a concept, change its inputs and follow the explanation. Each example models the stated rule or scenario; completing it is practice rather than evidence of mastery.
- Analog versus digital
- Sample intervals and rounding
- Bits, bytes and conventions
- Fixed-width versus AP integer model
Change it · step through · explain
Change an input, predict what will happen, then advance one step. Read why the state changes, reset and experiment. This fixed teaching model does not save progress or award XP.
Ready · Make a prediction
- ExploresamplingWaiting
- Sampling interval1Waiting
- Stored precisionwholeWaiting
Ready to explore: Sampling, precision and bit interpretation
Why: Change an input, predict the first effect, then advance one step.
Try this: Change one input or choose another listed case. Predict the effect, reset and compare the states and governing rule.
Step through and experiment
Change it · step through · explain
Change an input, predict what will happen, then advance one step. Read why the state changes, reset and experiment. This fixed teaching model does not save progress or award XP.
Ready · Make a prediction
- Input 145Waiting
- Input 26Waiting
Ready to experiment
Why: Predict the first change, then advance one step.
Try this: Try 63 and 64, then change the width.
Check a misconception
Claim: A digital record is an exact copy of every instant of a continuous source.
Finite sampling and precision omit detail even if every stored bit is intact.
Guided practice
Explain two ways this record can differ from the continuous temperature.
Work with a partner. Make a prediction, compare your reasoning, then identify the rule that supports your answer.
Independent transfer
Two programmes interpret 01000001 as 65 and A. Explain how both can be correct.
Exit check
What trade-off follows from storing more samples at finer precision?
Write your reasoning before comparing with a classmate. If your teacher assigned this task, submit it through My classes to save your work and receive feedback.
Check yourself
Your practice so far
Check an answer to see its rationale.