Mixed-base identity check: “12 (decimal) = 1101 (binary) = C (hexadecimal) = 0001 0010 (BCD).” Determine whether this chain of equalities is valid.

Introduction / Context:
Verifying equivalence across bases is a common skill in digital fundamentals. This item intentionally mixes correct and incorrect conversions to test careful checking of each representation: binary, hexadecimal, and packed BCD for the same decimal value 12.

Given Data / Assumptions:

• Target value: 12 decimal.
• Binary conversion must reflect base-2 positional weights.
• Hexadecimal C corresponds to 12 decimal.
• Packed BCD encodes each decimal digit in 4 bits.

Concept / Approach:
Evaluate each equality independently. Decimal 12 in binary is 1100 (8+4+0+0), not 1101 (which equals 13). Hexadecimal C equals 12, which is correct. Packed BCD for 12 is 0001 0010 (digit “1” → 0001; digit “2” → 0010), which is also correct. Therefore, because the binary term is wrong, the full chain is not valid.

Step-by-Step Solution:

Verification / Alternative check:
Convert the allegedly equal 1101 back to decimal: 18 + 14 + 02 + 11 = 13. Since this differs from 12, the chain fails. Two correct items (hex and BCD) cannot fix one wrong item (binary).

Why Other Options Are Wrong:

• Correct: Would require all representations to match 12; they do not.
• Correct only if parity/rounding: Parity and rounding are irrelevant to base conversion.
• Correct except for BCD: BCD part is actually correct; the binary is not.

Common Pitfalls:
Mistaking 1101 for 12 due to visual similarity; forgetting that BCD encodes decimal digits, not values directly; neglecting to recheck each piece independently.

Final Answer:
Incorrect