Definition check for BCD (binary-coded decimal): Do BCD digit encodings use only the 4-bit patterns from 0000 through 1001 (representing decimal 0–9), with the remaining 4-bit combinations considered invalid or unused for a single BCD digit?

Introduction / Context:
Binary-coded decimal (BCD) represents each decimal digit individually using a 4-bit group. Understanding which 4-bit patterns are valid BCD is essential when designing arithmetic units that operate on decimal digits or when validating user input in firmware and digital systems.

Given Data / Assumptions:

• Each BCD digit encodes a single decimal digit 0–9.
• A single 4-bit group is used per digit.
• Unused patterns must be detected or avoided in strict BCD contexts.

Concept / Approach:
Since there are 10 decimal digits and 16 possible 4-bit combinations, only 0000 through 1001 (0–9 decimal) are defined as valid BCD. The remaining combinations 1010 through 1111 do not represent single decimal digits in strict BCD and may be treated as invalid or used for special flags in some variants. Many hardware blocks implement decimal correction logic to ensure digit results remain within 0–9 during arithmetic operations like addition.

Step-by-Step Solution:

Verification / Alternative check:
Examine BCD adders: they perform binary add and then add 6 (0110) when the digit exceeds 1001 to restore a valid BCD range.

Why Other Options Are Wrong:
Including 1010 or 1011 as valid single digits contradicts strict BCD; limiting to 0000..0111 would exclude 8 and 9; two’s complement is unrelated to BCD digit validity.

Common Pitfalls:
Confusing BCD with packed formats that contain multiple digits per byte; forgetting to validate digits after arithmetic operations.

Final Answer:
Correct