Decimal to octal conversion exercise: What is the octal (base 8) equivalent of the decimal number 28₁₀?

Introduction / Context:
Converting decimal to octal is a standard number-system task in digital logic and computer organization. The repeated division method by the target base (here, 8) provides a reliable algorithm for the conversion.

Given Data / Assumptions:

• Given: 28 in base 10.
• Find: representation in base 8 (octal).
• Use integer division by 8 and collect remainders.

Concept / Approach:
Algorithm for decimal → octal: repeatedly divide the decimal number by 8, recording remainders at each step; the octal digits are these remainders read from last to first (bottom to top). This works because of place-value expansion in base 8.

Step-by-Step Solution:
28 ÷ 8 = 3 remainder 4 → least significant octal digit is 4.3 ÷ 8 = 0 remainder 3 → next digit is 3; division stops when quotient is 0.Read remainders upward: 3 4 → 34₈.

Verification / Alternative check:
Check by reconversion: 3*8 + 4 = 24 + 4 = 28, confirming 34₈ is correct.

Why Other Options Are Wrong:
32₈ = 26₁₀; 40₈ = 32₁₀; 36₈ = 30₁₀. Only 34₈ equals 28₁₀.

Common Pitfalls:
Reading remainders in the wrong order; confusing division quotients with remainders.

Final Answer:
348