What is the primary advantage of using Binary-Coded Decimal (BCD) instead of straight binary representation for decimal numbers?
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AFewer bits are required in BCD than in straight binary for all numbers
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BBCD codes are easily converted from decimal digits (and back)
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CThe relative ease of converting to and from decimal
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DBCD codes are always more storage-efficient than binary
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EBCD eliminates rounding errors in all numeric computations
Answer
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:
- BCD uses 4 bits per decimal digit (0000–1001 for 0–9).
- Straight binary represents the entire number in base-2 compactly.
- We are comparing representational advantages, not arithmetic performance.
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