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:
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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