Convert the octal number 47₈ to its binary equivalent by replacing each octal digit with its 3-bit binary form and concatenating the results.

Introduction / Context:Because one octal digit represents exactly three binary bits, converting octal to binary is direct and avoids decimal intermediates. This skill is essential when reading or writing low-level values in documentation or device registers that use octal notation.

Given Data / Assumptions:

• Octal input: 47₈ (digits 4 and 7).
• We use the fixed mapping from octal digits to 3-bit binaries.
• Leading zeros inside any digit’s 3-bit expansion must be preserved.

Concept / Approach:Map octal 4→100 and 7→111. Then concatenate the groups to form the final binary string. No padding beyond each digit’s 3-bit mapping is required when converting octal to binary.

Step-by-Step Solution:Write mappings: 4→100, 7→111.Concatenate: 100111.Append base: 100111₂.Select the matching option.

Verification / Alternative check:Decimal check: 47₈ = 4*8 + 7 = 39. Binary 100111₂ = 32 + 4 + 2 + 1 = 39. Values agree.

Why Other Options Are Wrong:110011₂ or duplicate entries: incorrect mapping for digits 4 and 7.1111011₂: too many bits; does not equal 39 in decimal.None: incorrect because 100111₂ is correct.

Common Pitfalls:Dropping leading zeros within a 3-bit group; reversing digit order; confusing hexadecimal (4-bit groups) with octal (3-bit groups).

Final Answer:100111₂