Convert the binary value 100011 (base 2) into its octal (base 8) representation. What is the correct octal result?

Introduction / Context:Binary-to-octal conversion is efficient because 1 octal digit maps exactly to 3 binary bits. Group the binary number into triples starting from the right (least significant bit), then translate each group to an octal digit.

Given Data / Assumptions:

• Binary value: 100011₂.
• We will group bits in sets of three from the right.
• No fractional parts; integer conversion only.

Concept / Approach:Write 100011₂ as grouped triples: 100 011. Convert each triple to octal: 100₂ = 4₈ and 011₂ = 3₈. Concatenate digits to obtain the octal number 43₈.

Step-by-Step Solution:

Verification / Alternative check:Decimal cross-check: 100011₂ = 32 + 2 + 1 = 35; 43₈ = 4*8 + 3 = 32 + 3 = 35. Both paths yield 35, so the conversion is correct.

Why Other Options Are Wrong:

Common Pitfalls:Failing to pad leftmost bits to a full group of three; using invalid octal digits (8 or 9).

Final Answer:43 (base 8)