Hexadecimal value to decimal and the role of parity: Compute the decimal value of 9E (hex). The phrase “odd parity” is incidental and does not alter the numeric value.

Difficulty: Easy

Correct Answer: 158

Explanation:


Introduction / Context:
Hexadecimal numbers are frequently converted to decimal for readability and to verify computations. Sometimes protocol fields mention parity for error checking, but parity does not change the numeric interpretation of a hexadecimal number itself. This question asks for the decimal value of 9E16 and clarifies that “odd parity” is not part of the numeric conversion.


Given Data / Assumptions:

  • Hex value: 9E16 (i.e., 0x9E).
  • Standard base conversion rules apply.
  • Parity, when mentioned, is a separate error-checking bit and not a component of the hexadecimal magnitude.


Concept / Approach:
Convert each hex digit to its decimal value and apply positional weights: the left digit is multiplied by 16^1 and the right digit by 16^0. The letter E corresponds to decimal 14. The sum gives the final decimal value.


Step-by-Step Solution:

Write 9E16 = 9 * 16^1 + E * 16^0.Compute 16^1 = 16 and 16^0 = 1.Substitute digits: 9 * 16 + 14 * 1 = 144 + 14.Add results: 144 + 14 = 158.


Verification / Alternative check:
Convert 158 back to hex: 158 / 16 = 9 remainder 14 → 9E16, confirming the conversion is correct.


Why Other Options Are Wrong:
30 and 78 are unrelated decimal values; saying “Nothing. Parity does not check.” confuses an integrity check with numeric conversion and is not a decimal value.


Common Pitfalls:
Treating E as 15 instead of 14; misinterpreting the parity comment as modifying the numeric value; reversing digit weights.


Final Answer:
158

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