Difficulty: Easy
Correct Answer: The relative ease of converting to and from decimal
Explanation:
Introduction / Context:
Binary-Coded Decimal (BCD) encodes each decimal digit using four bits, making it simple to map between human-readable decimal numbers and their digital representation. This question probes your understanding of why BCD is sometimes preferred despite its storage overhead compared to straight binary.
Given Data / Assumptions:
Concept / Approach:
The chief benefit of BCD is the direct digit-by-digit correspondence with decimal. Conversions to and from decimal display are straightforward and avoid complex base-2 to base-10 conversion routines. This is valuable in financial and UI-centric systems where decimal precision and display are frequent operations.
Step-by-Step Solution:
1) Identify what the question asks: the main advantage, not every advantage.2) Evaluate options: storage efficiency vs. conversion ease.3) BCD is less storage-efficient than binary (usually more bits).4) Therefore, the correct advantage is ease of decimal ↔ BCD conversion for each digit.
Verification / Alternative check:
Example: Decimal 59 → BCD digits 5 (0101) and 9 (1001) → 0101 1001. Converting back to decimal is trivial by reading each nibble; straight binary 59 (0011 1011) requires full base conversion to display digit characters.
Why Other Options Are Wrong:
Fewer bits required: false; BCD typically uses more bits.BCD always more efficient: incorrect; the opposite is common.BCD eliminates all rounding: arithmetic precision depends on algorithms; BCD helps with decimal rounding but does not eliminate all issues.
Common Pitfalls:
Assuming BCD is “better” universally; it is better only when decimal presentation or exact decimal digit control dominates. For computation, straight binary is usually smaller and faster.
Final Answer:
The relative ease of converting to and from decimal
Discussion & Comments