Validity of BCD codes — evaluate 10110110 as a binary-coded decimal value Binary-coded decimal (BCD) encodes each decimal digit separately using four bits (0000 to 1001 only). Which is the correct interpretation of the 8-bit BCD sequence 10110110?

Introduction / Context:
Binary-coded decimal (BCD) is a weighted code where each decimal digit 0–9 is represented by a 4-bit nibble. Because only 0000 through 1001 are valid for a single digit, any nibble from 1010 to 1111 indicates an invalid BCD encoding. This question checks your ability to validate BCD patterns and avoid accidental interpretation as straight binary.

Given Data / Assumptions:

• Given 8-bit pattern: 1011 0110.
• BCD validity requires each nibble to be in the range 0000–1001.
• Do not treat the entire 8 bits as a single binary number; treat as two BCD digits.

Concept / Approach:
Split the 8-bit code into high nibble and low nibble. Validate each nibble individually against the allowed BCD range. If either nibble falls outside 0000–1001, the overall 2-digit BCD value is invalid, regardless of what the straight-binary value would be.

Step-by-Step Solution:
Write the code as nibbles: 1011 0110.High nibble 1011 equals decimal 11, which is outside 0–9 and therefore invalid for BCD.Low nibble 0110 equals decimal 6, which is valid, but the presence of an invalid high nibble makes the entire BCD code invalid.Conclusion: the pattern is not a valid BCD number.

Verification / Alternative check:
Cross-check against a BCD table: only 0000–1001 represent digits 0–9. Codes 1010–1111 are forbidden in pure BCD. The leading nibble 1011 falls in the forbidden range, so the code is invalid.

Why Other Options Are Wrong:

• (a) 182: This would require a three-digit BCD; also, the high nibble cannot be 10 or 11.
• (b) 36: Would require nibbles 0011 0110; the given high nibble is 1011.
• (c) 116: Would require three BCD digits or an entirely different encoding.

Common Pitfalls:

• Interpreting the whole 8-bit pattern as straight binary. In straight binary, 10110110 is 182, but that is not how BCD works.
• Forgetting to validate each nibble independently.

Final Answer:
10110110 is not a valid BCD number.