Octal to binary conversion: Convert the octal number 134₈ to its binary representation, preserving leading zeros per octal-to-binary mapping.

Introduction / Context:Octal (base-8) digits map neatly to binary in groups of three bits because 8 = 2^3. Converting octal to binary is therefore a simple table-lookup process per digit.

Given Data / Assumptions:

• Octal number: 134₈.
• Digit mappings: 1→001, 3→011, 4→100.
• We keep each 3-bit group to avoid ambiguity.

Concept / Approach:Translate each octal digit to its 3-bit binary equivalent and concatenate in order. Leading zeros within a group are retained to preserve the 3-bit alignment that reflects the original octal digits.

Step-by-Step Solution:Map: 1→001, 3→011, 4→100.Concatenate: 001 011 100 → 001011100₂.

Verification / Alternative check:Convert back by grouping binary in 3s: 001→1, 011→3, 100→4 → 134₈. The cycle validates the result.

Why Other Options Are Wrong:(a) differs in the middle group, (b) mismaps groups, (d) discards necessary leading zeros and groups incorrectly.

Common Pitfalls:Omitting leading zeros in the leftmost group and misreading the resulting octal digits.

Final Answer:001011100₂.