Octal to binary via 3-bit groups Convert the octal number 5278 to binary (base 2) by mapping each octal digit to a 3-bit group.

Introduction / Context:
Octal and binary interconvert neatly because one octal digit corresponds to exactly three binary bits. Thus, conversion requires only a look-up per digit followed by concatenation—no arithmetic needed. We will convert 527_8 into binary using this 3-bit grouping rule.

Given Data / Assumptions:

• Octal input: 527 (base 8).
• Mapping: 0→000, 1→001, 2→010, 3→011, 4→100, 5→101, 6→110, 7→111.
• Leading zeros are kept per digit if needed.

Concept / Approach:

Translate each octal digit independently to its 3-bit binary equivalent, preserving order. Concatenate the results to obtain the final binary representation.

Step-by-Step Solution:

Verification / Alternative check:

Convert back by regrouping the binary into 3-bit chunks from the right: 101 010 111 → 5 2 7 in octal. Round-trip confirms correctness.

Why Other Options Are Wrong:

011100111 and 111010101 rearrange groups, not matching the digit-wise mapping.

343 is neither a binary string nor a valid base-2 representation; it is a decimal-looking number.

Common Pitfalls:

Dropping leading zeros in a 3-bit group (e.g., 2 should be 010, not 10), or reversing digit order. Keep exactly three bits per octal digit to avoid ambiguity.

Final Answer:

101010111