Decimal to octal conversion: What is the octal (base 8) equivalent of the decimal number 42₁₀?

Introduction / Context:
Number base conversion is a foundational skill in digital systems. Converting decimal to octal can be accomplished using repeated division by 8, collecting remainders that become the octal digits (least significant first).

Given Data / Assumptions:

• Given: 42 in base 10.
• Wanted: representation in base 8.
• Use integer division and remainder arithmetic.

Concept / Approach:
The value of a number in base 8 is the sum of digits times powers of 8. Repeated division by 8 yields remainders in 0–7 which form the octal digits from right to left, ensuring correct place-value reconstruction.

Step-by-Step Solution:
42 ÷ 8 = 5 remainder 2 → least significant digit = 2.5 ÷ 8 = 0 remainder 5 → next digit = 5 (stop since quotient is 0).Read upwards: 5 2 → 52₈ (written as 528).

Verification / Alternative check:
Check: 5*8 + 2 = 40 + 2 = 42, confirming the correctness of 52₈.

Why Other Options Are Wrong:
57₈ = 47₁₀; 42₈ = 34₁₀; 47₈ = 39₁₀. Only 52₈ equals 42₁₀.

Common Pitfalls:
Writing digits in the wrong order (top-to-bottom instead of bottom-to-top) or mixing up quotient and remainder.

Final Answer:
528