Correct option is D
In 8421 BCD, only the binary patterns for decimal 0–9 are valid: 0000–1001.
The six remaining 4-bit combinations—1010 (10) to 1111 (15)—do not represent any decimal digit in standard BCD.
When drawing a K-map for BCD logic, these invalid codes are restricted (unused) and are typically treated as don’t-cares (X) for simplification.
Using them as X allows forming larger groups, yielding simpler POS/SOP expressions.
Hence, BCD digits are restricted from 1010 through 1111.
When drawing a K-map for BCD logic, these invalid codes are restricted (unused) and are typically treated as don’t-cares (X) for simplification.
Using them as X allows forming larger groups, yielding simpler POS/SOP expressions.
Hence, BCD digits are restricted from 1010 through 1111.
Important Key Points
- BCD Range: Valid codes = 0000–1001 (decimal 0–9).
- Invalid Set: 1010–1111 correspond to 10–15 (not used in standard BCD).
- K-map Practice: Mark invalid codes as don’t-cares to simplify logic.
- Why 8421: Weighted code (8,4,2,1) mapping each decimal digit to 4 bits.
- Design Impact: Exploiting don’t-cares reduces gate count and complexity.
- Consistency: Ensure circuits never generate these invalid inputs during normal operation.
Knowledge Booster
- Why not (a) or (b)? These ranges include many valid BCD codes (0–9), so they can’t be the restricted set.
- Why not (c)? Stops at 1110, omitting 1111, which is also invalid; thus incomplete.
- Extra tip: Non-8421 BCD variants exist (e.g., Excess-3), but standard BCD always treats 10–15 as invalid.
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