8421 BCD Counter — Identify an Invalid Output State Which of the following is an invalid output state for a 4-bit 8421 BCD counter stage?

Introduction / Context:
An 8421 BCD counter encodes decimal digits 0 through 9 using a 4-bit binary code. Only ten patterns are valid (0000 to 1001). Recognizing invalid states is essential for designing decode logic and for ensuring that counters recover correctly from power-up or noise-induced illegal states.

Given Data / Assumptions:

• Valid BCD codes: 0000–1001.
• Invalid BCD codes: 1010–1111.
• 8421 weighting implies standard BCD, not excess-3 or other variants.

Concept / Approach:
To identify an invalid state, check whether the 4-bit pattern represents a decimal digit greater than 9. Any pattern with the two MSBs equal to 11 (i.e., 12–15) is invalid for 8421 BCD. Likewise, 1010 (10) through 1101 (13) are also invalid.

Step-by-Step Solution:
List options: 1110, 0000, 0010, 0001.Evaluate validity: 0000 (0), 0001 (1), 0010 (2) are valid BCD codes.Evaluate 1110: equals decimal 14, which is not a valid BCD digit.Thus, 1110 is an invalid BCD counter output.

Verification / Alternative check:
Consult any BCD truth table: codes from 0000 to 1001 are valid; 1110 falls outside the permitted range.

Why Other Options Are Wrong:

• 0000: valid BCD for 0.
• 0010: valid BCD for 2.
• 0001: valid BCD for 1.

Common Pitfalls:
Confusing 8421 BCD with other decimal codes (e.g., Gray or excess-3), or assuming all 4-bit patterns are acceptable for BCD.

Final Answer:
1110