Binary-coded decimal (BCD): each decimal digit is represented using how many bits in standard BCD encoding?

Difficulty: Easy

Correct Answer: One nibble (4 bits)

Explanation:


Introduction / Context:
Binary-coded decimal (BCD) is a numeric encoding in which each decimal digit (0 through 9) is encoded separately in binary. BCD is widely used in calculators, financial displays, and any system where exact decimal digit representation and easy decimal I/O are important.


Given Data / Assumptions:

  • We are discussing standard straight (8421) BCD.
  • Valid digit codes range from 0000 (0) to 1001 (9).
  • Upper binary combinations 1010–1111 are invalid in straight BCD.


Concept / Approach:
Standard BCD uses 4 bits per decimal digit. Each 4-bit group (a nibble) holds one digit. Multi-digit numbers are encoded as sequences of nibbles, not as a single pure-binary value. This facilitates easy conversion to human-readable decimal digits and prevents rounding errors that can occur with binary floating formats when decimal exactness is required.


Step-by-Step Solution:

Identify the unit of encoding in BCD: one decimal digit per group. Confirm bit-width: straight BCD maps 0–9 to 0000–1001, which fits in 4 bits. Therefore, each digit uses one nibble (4 bits).


Verification / Alternative check:
Check common examples: 59 in BCD is 0101 1001 (two nibbles), not 00111011 (which is binary 59). This reaffirms the 4-bit-per-digit rule.


Why Other Options Are Wrong:

One byte (8 bits): too large per digit; wastes space for straight BCD. One bit: insufficient, since a digit can be 0–9, needing at least 4 bits. All of the above: contradictory; only 4 bits is correct. None: invalid because the nibble answer is correct.


Common Pitfalls:
Confusing BCD with packed or unpacked representations: unpacked BCD may use a full byte per digit for convenience, but the encoding itself still uses 4 bits to carry the value 0–9.


Final Answer:
One nibble (4 bits)

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