lesson
A carry still has place value
1 · Learn
Binary addition uses the same place-value idea as decimal addition, but a column carries when it reaches two rather than ten. Thus 1 + 1 gives binary 10, and 1 + 1 + 1 gives binary 11.
A fixed number of bits has a limited range. A result needing another bit may overflow that representation; do not silently discard the extra bit and claim the exact result is unchanged.
2 · Worked example
0011 + 0101 = 1000, matching decimal 3 + 5 = 8. A four-bit unsigned value cannot represent decimal 16 without an extra bit.
3 · Your turn
Add 0110 and 0011 in binary. What decimal calculation checks it?
Check your answer
1001; 6 + 3 = 9.
4 · Apply your learning
Trace carries on paper, then test a sum that exceeds four bits and explain the representation limit.
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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