BCD addition rule: Evaluate the BCD sum of 0101 (5) and 0100 (4). Is the result 0000 1001 (i.e., 00001001 BCD)?

Introduction / Context:Binary-coded decimal (BCD) encodes each decimal digit in a 4-bit nibble. We add 5 (0101) and 4 (0100) and verify the BCD correction rules and final encoding.

Given Data / Assumptions:

• Operands are single-digit BCD values: 0101 and 0100.
• We use standard BCD correction (add 0110 when a nibble exceeds 1001).
• We present the result in 8-bit form as 0000 1001 for a one-digit sum.

Concept / Approach:First perform binary addition of the low nibble. If the nibble sum is greater than 1001 (9) or a carry is generated, add 0110 to correct to valid BCD. Here, 0101 + 0100 = 1001 (9), which is already a valid BCD digit; no correction is needed.

Step-by-Step Solution:

Verification / Alternative check:Decimal check: 5 + 4 = 9 → BCD 1001; extended to 8 bits as 0000 1001.

Why Other Options Are Wrong:

Common Pitfalls:Applying BCD correction even when the nibble is already valid.

Final Answer:Correct