BCD digit range — Identify the largest valid decimal digit that can be represented by a single 4-bit Binary-Coded Decimal (BCD) nibble.
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
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A9
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B10
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C15
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D16
Answer
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.Final Answer:
9