Octal conversion — base-10 to base-8 Convert the decimal number 39 (base 10) into octal (base 8).

Introduction / Context:
Octal (base 8) is often used to compactly represent binary on systems aligned to 3-bit groups. Converting a decimal number to octal can be done via repeated division by 8, collecting remainders. We will convert 39 to octal and verify via back-conversion to decimal for confidence.

Given Data / Assumptions:

• Input: 39 in base 10.
• Octal digits range: 0–7.
• We expect a two-digit octal result for this small number.

Concept / Approach:

Use repeated division by 8. The octal digits are the remainders read in reverse order (last remainder becomes the most significant digit). Alternatively, recognize that 39 = 48 + 7 at a glance.

Step-by-Step Solution:

Verification / Alternative check:

Convert 47_8 back: 48 + 7 = 39. The round trip confirms correctness.

Why Other Options Are Wrong:

638 and 748: include digits 8 or 9? (not here, but their values don't map to 39 when interpreted as octal strings presented).

368: digits are valid but equals 364 + 68 + 8? (format confusion). The correct two-digit octal for 39 is simply 47.

Common Pitfalls:

Writing remainders in the wrong order or confusing base markers. Always read remainders from last to first when finishing the division chain.

Final Answer:

478