Division-by-two method nuance: “When converting decimal to binary using repeated division by 2, the first remainder obtained becomes the most significant bit (MSB).” Judge this statement.

Introduction / Context:
The repeated division-by-two algorithm is a staple for manual decimal-to-binary conversion. Correct bit ordering is crucial. This question probes whether the learner knows which remainder becomes the least significant bit (LSB) and which becomes the most significant bit (MSB).

Given Data / Assumptions:

• We repeatedly divide the decimal number by 2 and record remainders (0 or 1).
• Remainders are produced from least significant position upward.
• The final remainder corresponds to the MSB when read in reverse order.

Concept / Approach:
Each division by 2 peels off the current LSB. Thus, the very first remainder is the LSB, not the MSB. The sequence of remainders, when read from last to first, yields the correct binary digits from MSB to LSB.

Step-by-Step Solution:

Verification / Alternative check:
Example: 13. Divisions yield remainders 1, 0, 1, 1. Writing them in reverse gives 1101, which is the binary for 13. The first remainder (1) is clearly the LSB at the rightmost end, not the MSB.

Why Other Options Are Wrong:

• Correct: Misstates the ordering; the first remainder is LSB.
• Other distractors (hex, signed magnitude, Gray code): Unrelated to the division-by-two remainder ordering.

Common Pitfalls:
Listing remainders in the order computed without reversing; confusing modulus operation output position; mixing methods (e.g., subtraction of powers of two) with division-by-two and conflating their steps.

Final Answer:
Incorrect