lesson
Two symbols can represent many values
1 · Learn
Binary uses digits 0 and 1. For whole numbers, places from right to left have values 1, 2, 4, 8, 16 and so on. Add the place values containing 1. A bit is one binary digit; eight bits form a byte.
A binary pattern's meaning depends on how it is interpreted. The same bits might encode a number, a character or part of an image under different agreed formats.
2 · Worked example
Binary 1011 has 8 + 0 + 2 + 1 = 11 in decimal. Binary 0101 represents 5; the leading zero does not add value.
3 · Your turn
Convert binary 1101 to decimal and decimal 6 to four-bit binary.
Check your answer
13; 0110.
4 · Apply your learning
Use four labelled place cards to represent every value from 0 to 15 and explain why a fifth bit extends the range.
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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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