Exam-style question
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Convert 219₁₀ into binary and hexadecimal. Show the method used for both conversions.
Model answer
What a good answer should say
- 219₁₀ = 11011011₂ = DB₁₆.
- For binary, use the place values 128, 64, 32, 16, 8, 4, 2 and 1.
- The value 219 is 128 + 64 + 16 + 8 + 2 + 1, giving 11011011₂.
- For hexadecimal, split the binary number into two groups of four: 1101 1011.
Explanation
Why this works
The binary expansion must add to 219. Grouping binary digits into fours provides a direct hexadecimal conversion because each hexadecimal digit corresponds to exactly four binary digits.
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