Decimal → binary method — evaluate the statement: “Decimal numbers can be converted into binary by dividing by 2 repeatedly and recording the remainders (LSB first).” Is this standard algorithm description accurate?

Introduction / Context:One of the most taught methods for decimal-to-binary conversion in digital fundamentals is the repeated division-by-2 technique. It yields binary digits as remainders, naturally generating the least significant bit first. This question checks whether that description accurately captures the process.

Given Data / Assumptions:

• Unsigned integer conversion is considered.
• Remainders from successive divisions by 2 are either 0 or 1.
• The final binary number is read from the last remainder to the first (reverse order).

Concept / Approach:Division by the base (2) produces digits in reverse order. Each division step produces a quotient and a remainder; stacking remainders from last to first reconstructs the binary representation. This method is efficient for manual conversions and is analogous to division by 8 for octal and by 16 for hexadecimal.

Step-by-Step Solution:

Verification / Alternative check:Example: 13 ÷ 2 → r1; 6 ÷ 2 → r0; 3 ÷ 2 → r1; 1 ÷ 2 → r1; reading remainders backward gives 1101 (binary for 13). The procedure works for any nonnegative integer.

Why Other Options Are Wrong:

• Incorrect: Conflicts with a universally taught algorithm.
• “Applies only to even numbers” / “only up to 8 bits”: The method is general; the number of bits expands as needed.

Common Pitfalls:Forgetting to reverse the order of remainders; mishandling 0 and 1 edge cases; confusing integer division with floating-point division for fractional parts (which require a separate multiply-by-2 method).

Final Answer:Correct — repeated division by 2 with recorded remainders is the standard decimal-to-binary conversion method.