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

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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. Final Answer: 9

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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