Detecting invalid BCD digits Which 4-bit pattern below is not a valid Binary-Coded Decimal (BCD) code for a single decimal digit?

Difficulty: Easy

Correct Answer: 1101

Explanation:


Introduction / Context:
BCD encodes each decimal digit (0–9) as a 4-bit binary value. Recognizing valid versus invalid 4-bit patterns is essential for input validation, display drivers, and error checking in digital systems that use BCD instead of pure binary.


Given Data / Assumptions:

  • Valid BCD digit range: 0000 through 1001 (0 to 9).
  • Invalid patterns are any 4-bit values from 1010 to 1111.
  • We evaluate each option against these ranges.


Concept / Approach:
Check whether the given 4-bit code is less than or equal to 1001. If it exceeds 1001, it cannot represent a decimal digit in BCD and is therefore invalid.


Step-by-Step Solution:

1) 0011 → decimal 3: valid.2) 0101 → decimal 5: valid.3) 1001 → decimal 9: valid.4) 1101 → decimal 13: not a valid BCD digit (invalid).


Verification / Alternative check:
List all invalid BCD codes: 1010, 1011, 1100, 1101, 1110, 1111. 1101 is in this set.


Why Other Options Are Wrong:

  • 0011, 0101, 1001: all lie within 0000–1001 and therefore are valid BCD digits.


Common Pitfalls:
Confusing BCD with hexadecimal, where 1010–1111 would be valid (A–F). In BCD, those patterns are illegal for single digits.


Final Answer:
1101

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