BCD encoding — Write the Binary-Coded Decimal (BCD) representation for the decimal number 474 (three digits).

Difficulty: Easy

Correct Answer: 0100 0111 0100

Explanation:


Introduction / Context:
Binary-Coded Decimal (BCD) stores each decimal digit using its 4-bit binary equivalent. It is commonly used with numeric displays and in financial or human-facing arithmetic where exact decimal representation is desirable. The task is to encode 474 in BCD.

Given Data / Assumptions:

  • Decimal digits: 4, 7, and 4.
  • BCD digit mappings: 4 → 0100, 7 → 0111.
  • Each digit is encoded independently and then concatenated.


Concept / Approach:
Convert each decimal digit to its 4-bit binary value (0–9 only) and place them in order. No arithmetic is performed on the magnitude as a whole; BCD preserves decimal digit boundaries.

Step-by-Step Solution:

Convert hundreds digit 4 → 0100.Convert tens digit 7 → 0111.Convert ones digit 4 → 0100.Concatenate: 0100 0111 0100.


Verification / Alternative check:

Check each 4-bit group is within 0000–1001; all groups are valid BCD codes.


Why Other Options Are Wrong:

Option B contains 1011, which equals decimal 11 and is invalid for a single BCD digit.Option C includes 1001 (9) and 0011 (3), which would encode 493, not 474.Option D mixes 0110 (6), 1011 (invalid), and 1001 (9) and does not represent 474.


Common Pitfalls:

Treating BCD like pure binary of the entire number; BCD encodes digits individually.Allowing 1010–1111 in a digit position, which are invalid in standard BCD.


Final Answer:

0100 0111 0100

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