Convert the base 4 number 312₄ to base 8.
Answer and explanation
Correct answer: D. 66₈
- Step 1: Convert 312₄ to base 10: 3(4²) + 1(4¹) + 2(4⁰) = 3(16) + 4 + 2 = 48 + 6 = 54₁₀. Step 2. Convert 54₁₀ to base 8: 54 ÷ 8 = 6 with remainder 6. Step 3. Reading remainders gives 66₈. Answer: 66₈. Why not the others: 54₈ confuses base 10 with base 8; 72₈ and 62₈ represent division remainder errors.
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