lesson
Formats give bits their meaning
1 · Learn
Text can be represented by character codes; an image can be represented by pixel colour values; digital sound can be represented by measurements of a signal taken over time. These are different encoding schemes, not different kinds of bit.
More pixels or more detailed samples can require more data, but quality also depends on the source and method. Enlarging a low-detail image does not automatically recreate missing detail.
2 · Worked example
A tiny black-and-white model image has one bit per pixel. A 4 by 3 grid needs 12 pixel bits before any headers or metadata in this simplified uncompressed model.
3 · Your turn
In the stated one-bit-per-pixel model, how many pixel bits does an 8 by 5 image need?
Check your answer
40 bits, excluding headers, metadata or other storage overhead.
4 · Apply your learning
Encode and decode a small invented monochrome grid using an explicitly agreed order for its pixels.
Adult guidance and safety
Use an approved private programming or authoring environment and fictional data. Do not install unknown software or enter personal credentials for these exercises. Trace first, then run and test where a suitable tool is available; these text examples do not themselves provide an executable assessment environment.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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