Introduction / Context:
BCD encodes each decimal digit (0–9) as its own 4-bit binary pattern, making it ideal for interfaces where humans read or enter decimal numbers. This question clarifies the real motivation for BCD, countering common misconceptions about efficiency.
Given Data / Assumptions:
- BCD maps exactly one decimal digit per 4-bit nibble.
- Human interfaces (keypads, seven-segment displays, printers) expect decimal digits.
- Arithmetic speed and storage efficiency are not BCD’s strengths.
Concept / Approach:
BCD simplifies the conversion between internal representation and human-readable decimal digits. It enables easy driving of decimal displays via simple decoders and straightforward acceptance of digit-wise input, avoiding complex binary-to-decimal conversions in real time.
Step-by-Step Solution:
Identify interface need: humans use base-10.Match representation: BCD represents each digit directly, simplifying decoding/encoding.Acknowledge trade-offs: BCD uses more bits than binary and arithmetic can be slower.Thus, the primary reason is user-facing alignment, not arithmetic efficiency.
Verification / Alternative check:
Consider a calculator display driver or seven-segment interface: BCD-to-7-segment ICs accept BCD directly.
Why Other Options Are Wrong:
It is too easy arithmetically: BCD arithmetic is typically more complex than binary.Minimizes storage: BCD is less space-efficient than pure binary.Maximizes speed: Binary arithmetic in ALUs is generally faster.
Common Pitfalls:
Assuming “ease of use by people” translates to “ease of arithmetic by machines”.Overlooking conversion/driver simplicity provided by BCD.
Final Answer:
It aligns directly with decimal digits for display and entry
Discussion & Comments