Difficulty: Medium
Correct Answer: 0001 0010 0100 0000
Explanation:
Introduction / Context:
Binary-coded decimal (BCD) represents each decimal digit with its own 4-bit code, which is common in digital displays and decimal arithmetic units. This task checks your ability to encode, add, and recognize the BCD result.
Given Data / Assumptions:
Concept / Approach:
Add the decimal numbers first to know the expected result, then encode that result into BCD. Alternatively, convert each operand to BCD, add digit-wise, and apply a +6 correction (0110) to any digit sum greater than 9 to restore valid BCD and propagate carries.
Step-by-Step Solution:
Verification / Alternative check:
Digit-wise BCD add: 5 + 5 = 10 → write 0, carry 1; 7 + 6 + 1 = 14 → write 4, carry 1; 2 + 9 + 1 = 12 → write 2, carry 1 to thousands → 1. Encoded result is identical to the direct conversion of 1240.
Why Other Options Are Wrong:
Common Pitfalls:
Final Answer:
0001 0010 0100 0000
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