Maximum single-digit value in BCD: For a single BCD digit, is the largest valid value equal to binary 1111 (decimal 15), or is the maximum decimal digit 9 represented as 1001?

Introduction / Context:
BCD encodes each decimal digit using four bits, but not all 4-bit combinations are legal for a single digit. This question examines whether the maximum single-digit BCD value can be 1111 (15) or whether the largest valid digit is 9 (1001).

Given Data / Assumptions:

• Single-digit BCD must represent decimal 0–9 only.
• Each digit uses exactly 4 bits.
• Values beyond 9 are invalid for a single BCD digit.

Concept / Approach:
Since decimal digits range from 0 to 9, the largest valid BCD digit is 9, encoded as 1001. The 4-bit patterns 1010 through 1111 do not represent single decimal digits in strict BCD and are considered invalid or reserved. This restriction ensures correct decimal arithmetic and encoding for display and storage of decimal values.

Step-by-Step Solution:

Verification / Alternative check:
Consult standard BCD adders: after binary addition, results greater than 1001 require adding 0110 to re-normalize into valid BCD range, confirming that 10–15 are invalid per-digit values.

Why Other Options Are Wrong:
Marking “Correct” would imply 15 is valid, which contradicts BCD rules; “packed BCD,” “signed BCD,” or “endian format” do not change the per-digit validity constraint.

Common Pitfalls:
Treating a 4-bit field as an unrestricted binary number instead of a BCD digit; misinterpreting formatting (packed vs unpacked) as altering allowed digit encodings.

Final Answer:
Incorrect