Identifying invalid states in an 8421 BCD counter Which of the following 4-bit codes is an invalid state for a natural 8421 BCD up-counter?

Introduction / Context:
BCD (binary-coded decimal) in 8421 weighting represents decimal digits 0 through 9 using 4-bit codes from 0000 to 1001. States 1010 through 1111 are not valid BCD digits and are skipped or corrected in BCD counters. Recognizing valid versus invalid states is important for designing truncation and reset logic.

Given Data / Assumptions:

• 8421 BCD valid range: 0000 (0) to 1001 (9).
• Invalid range: 1010 (10) to 1111 (15).
• We check the listed codes against these ranges.

Concept / Approach:
Compare each option to the valid set. Codes representing decimal 0–9 are valid; anything above 1001 is invalid in a pure BCD digit counter and must be corrected via synchronous clear or carry logic when designing counters or state machines that display decimal digits.

Step-by-Step Solution:

Verification / Alternative check:
Check any BCD truth table: only 0000–1001 are mapped to digits; 1100 is unmapped and thus invalid.

Why Other Options Are Wrong:

• 0011, 1001, 1000: All within 0–9 and therefore legal BCD states.

Common Pitfalls:
Confusing 8421 with other BCD variants; forgetting that counters must skip or reset on reaching 1010 (decimal 10) to maintain decimal correctness.

Final Answer:
1100