BCD addition: Compute the BCD sum of 0101 (5) and 0110 (6). Provide the result as a two-digit BCD codeword.

Introduction / Context:
Binary Coded Decimal (BCD) represents each decimal digit with its 4-bit binary equivalent. BCD addition requires special handling whenever a 4-bit nibble exceeds 9 or produces a carry, applying a decimal correction (add 6) to maintain valid BCD digits.

Given Data / Assumptions:

• Operands: 0101 (decimal 5) and 0110 (decimal 6).
• We want a two-digit BCD result.
• Use standard BCD correction rules.

Concept / Approach:
Add the nibbles as binary; if the sum > 1001 (9) or a carry occurs, add 0110 (6) to correct the nibble and propagate carry to the next decimal digit. This ensures each nibble remains a valid BCD 0000–1001.

Step-by-Step Solution:

Verification / Alternative check:
Decimal check: 5 + 6 = 11; BCD “11” is 0001 0001. No ambiguity remains.

Why Other Options Are Wrong:

• 00010111BCD: Intermixes carry and nibble incorrectly.
• 00001009BCD: Not valid; option text shows 00001001BCD (9), which does not equal 11.
• 00010011BCD: 13 in BCD, not 11.

Common Pitfalls:
Forgetting the +6 correction; misplacing the carry bit; confusing raw binary sum with BCD-corrected digits.

Final Answer:
00010001BCD