Exam-style question
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Convert 3A₁₆ into decimal and binary. Explain how the hexadecimal digits help with the binary conversion.
Model answer
What a good answer should say
- 3A₁₆ = 58₁₀ = 00111010₂.
- In decimal, 3A₁₆ = (3 × 16) + 10 = 48 + 10 = 58₁₀.
- For binary, 3₁₆ is 0011₂ and A₁₆ is 1010₂, so 3A₁₆ = 00111010₂.
Explanation
Why this works
The hexadecimal digit A has the decimal value 10. Each hexadecimal digit can be replaced by a four-bit binary group, so the conversion to binary is direct and preserves leading zeroes within each group.
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