Octal to binary conversion: Convert the octal number 60₈ into binary and choose the correct binary representation.

Introduction / Context:Bases 8 and 2 are closely related because 8 = 2^3. Therefore, each octal digit maps to exactly three binary bits. This makes octal ↔ binary conversion especially quick and reliable without passing through decimal.

Given Data / Assumptions:

• Octal input: 60₈.
• Binary output is required.
• We will map each octal digit to a 3-bit binary group.

Concept / Approach:Use the mapping: 0 → 000, 1 → 001, 2 → 010, 3 → 011, 4 → 100, 5 → 101, 6 → 110, 7 → 111.

Step-by-Step Solution:Write octal digits: 6 and 0.Map 6 → 110 and 0 → 000.Concatenate groups: 110000₂.

Verification / Alternative check:Convert to decimal for a cross-check: 60₈ = 6*8 + 0 = 48; binary 110000₂ also equals 32 + 16 = 48. They match.

Why Other Options Are Wrong:10011₂ (19), 1100111₂ (103), and 1100110₂ (102) do not equal 48.

Common Pitfalls:Forgetting to keep three bits per octal digit or dropping leading zeros for interior digits (though leading zeros on the far left can be omitted).

Final Answer:110000₂.