Binary-coded decimal (BCD) storage width: How many bits are used to store a single BCD digit (that is, one decimal digit encoded in BCD)?

Introduction / Context:
Binary-coded decimal (BCD) is widely used in digital systems that need to display or process human-readable decimal digits, such as clocks, calculators, meters, and financial devices. Knowing the encoding width for one BCD digit is essential for estimating memory, designing buses, and mapping between binary arithmetic and decimal display logic.

Given Data / Assumptions:

• BCD encodes one decimal digit 0–9.
• We seek the number of bits required per digit in standard straight BCD (8421 code).
• No packed-nibble vs. unpacked-byte trickery is implied; the question is about the minimal code width.

Concept / Approach:
Standard straight BCD uses a 4-bit nibble to represent each decimal digit. The 4 bits are often labeled with weights 8-4-2-1 (8421). Ten valid patterns (0000 to 1001) represent digits 0 to 9, while 1010 to 1111 are invalid or used in special variants. Systems may store two BCD digits in one 8-bit byte (packed BCD), but per-digit encoding is still 4 bits.

Step-by-Step Solution:

Verification / Alternative check:
Check common devices: seven-segment drivers, RTC chips, and microcontroller libraries all treat each decimal digit as a nibble, frequently packing two digits into a byte for efficient storage.

Why Other Options Are Wrong:

• 8: One byte is used to store two BCD digits when packed; not per digit.
• 1 or 2: Too few states to represent ten symbols.

Common Pitfalls:
Confusing packed BCD storage (two digits per 8-bit byte) with the number of bits per digit, and assuming a pure binary representation rather than digit-wise encoding.

Final Answer:
4