Number systems — converting decimal fractions to binary: Consider the specific case of converting a decimal fraction (the part to the right of the decimal point, such as 0.625) into its binary representation. Evaluate the statement: “A decimal fraction can be converted to binary by using the repeated division-by-2 method.”

Introduction / Context:
Converting between number systems is a core digital design skill. While repeated division-by-2 works perfectly for the integer part of a decimal number, the fractional part follows a different algorithm. This item checks whether you can distinguish the correct technique for decimal fractions versus integers when moving to binary.

Given Data / Assumptions:

• We are converting a pure decimal fraction (e.g., 0.625) or the fractional portion of a mixed number (e.g., 12.625).
• No rounding unless stated; assume enough iterations to reach an exact or acceptably precise value.
• Standard unsigned fixed-point interpretation is used.

Concept / Approach:
For the integer part, use repeated division by 2 and collect remainders. For the fractional part, use repeated multiplication by 2 and collect the integer bits that appear at each step. Therefore, “division-by-2” is not the method for fractions; “multiplication-by-2” is.

Step-by-Step Solution:
Example: Convert 0.625 to binary by repeated multiply-by-2.0.625 * 2 = 1.25 → bit 1 (keep 0.25)0.25 * 2 = 0.5 → bit 0 (keep 0.5)0.5 * 2 = 1.0 → bit 1 (keep 0) → result .101Combine with integer part if present using division-by-2 for the integer portion.

Verification / Alternative check:
Cross-check: .101₂ = 1/2 + 0 + 1/8 = 0.625, confirming the multiply-by-2 approach is correct for fractions.

Why Other Options Are Wrong:
“Correct” confuses integer and fractional algorithms. Scientific notation or signed-magnitude does not change the fundamental multiply-by-2 rule for fractional conversion.

Common Pitfalls:
Mixing the integer method (division) with the fractional method (multiplication); stopping iterations too early and introducing rounding errors without noting precision.

Final Answer:
Incorrect