Octal-to-binary conversion rule — verify bit-grouping: Assess the statement: “Octal-to-binary conversion is accomplished by simply replacing each octal digit with its 4-bit binary equivalent.”

Introduction / Context:
Understanding clean mappings between bases helps with quick conversions and reading legacy code or documentation. Octal (base-8) relates naturally to binary via 3-bit groupings, while hexadecimal relates via 4-bit groupings.

Given Data / Assumptions:

• Octal digits range from 0 to 7.
• Binary grouping should exactly cover the range of each digit.
• No arithmetic conversion is necessary if grouping is correct.

Concept / Approach:
Since 2^3 = 8, each octal digit maps to a 3-bit binary pattern from 000 to 111. Therefore, octal-to-binary conversion proceeds by replacing each octal digit with a 3-bit equivalent, not 4 bits. The 4-bit (nibble) mapping applies to hexadecimal (2^4 = 16), not octal.

Step-by-Step Solution:
Take an octal numeral, e.g., 725₈.Convert each digit: 7→111, 2→010, 5→101.Concatenate: 111 010 101₂ (optionally pad leftmost group).This direct substitution confirms the 3-bit rule.

Verification / Alternative check:
Reverse mapping: group binary in triples and translate back to octal digits 0–7; this recovers the original octal numeral.

Why Other Options Are Wrong:
“Correct” confuses octal with hex; restricting the claim to certain digits or suppressing zeros does not change the fundamental 3-bit mapping.

Common Pitfalls:
Forgetting to pad the most significant group with leading zeros to complete a triple; mixing 3-bit (octal) and 4-bit (hex) groupings in the same conversion.

Final Answer:
Incorrect (use a 3-bit binary group per octal digit)