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BCD digit range — Identify the largest valid decimal digit that can be represented by a single 4-bit Binary-Coded Decimal (BCD) nibble.

Difficulty: Easy

Correct Answer: 9

Explanation:

Introduction / Context:
Binary-Coded Decimal (BCD) encodes each decimal digit into a 4-bit group for ease of decimal display and arithmetic adjustments. Understanding the valid range of a single BCD nibble is essential for detecting invalid codes and designing BCD adders or display drivers.

Given Data / Assumptions:

One BCD digit uses exactly 4 bits.
Valid BCD patterns represent decimal 0 through 9 inclusive.
Bit patterns 1010 through 1111 are invalid in standard BCD.

Concept / Approach:
Because BCD mirrors decimal digits, the highest allowable decimal value in one nibble is 9. Although 4 bits can represent 0–15 in pure binary, BCD reserves only 10 codes for 0–9 and treats 10–15 as illegal for a single decimal digit.

Step-by-Step Solution:

Recognize the mapping: 0000→0, 0001→1, …, 1001→9.Identify the largest decimal digit that is still valid: 9.Confirm that 1010–1111 are invalid in standard BCD.

Verification / Alternative check:

Consult any BCD truth table or seven-segment decoder inputs; codes above 1001 are undefined or flagged as invalid.

Why Other Options Are Wrong:

10: Requires two BCD digits (1 and 0), not one nibble.15 and 16: Not representable as a single BCD digit; 16 is outside 4-bit decimal digit range entirely.

Common Pitfalls:

Assuming a 4-bit field always permits values up to 15; BCD intentionally restricts the set.Confusing packed BCD (two digits per byte) with pure binary bytes.

BCD digit range — Identify the largest valid decimal digit that can be represented by a single 4-bit Binary-Coded Decimal (BCD) nibble.

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