Base conversion — Convert the hexadecimal number AA (base 16) to its decimal (base 10) value.

Difficulty: Easy

Correct Answer: 170

Explanation:


Introduction / Context:
Hexadecimal AA is a common test case because both digits are A, which equals 10 in decimal. Converting it correctly demonstrates comfort with base-16 positional arithmetic.

Given Data / Assumptions:

  • A_hex = 10_decimal.
  • AA_hex = A16^1 + A16^0.
  • 16^1 = 16, 16^0 = 1.


Concept / Approach:
Multiply each hex digit value by its positional weight and add. Since both digits are 10, the computation is straightforward: 1016 + 10.

Step-by-Step Solution:

Evaluate high digit: 10 * 16 = 160.Evaluate low digit: 10 * 1 = 10.Sum: 160 + 10 = 170.


Verification / Alternative check:

Binary check: AA_hex = 1010 1010₂ = 128 + 32 + 8 + 2 = 170.


Why Other Options Are Wrong:

165: Would correspond to 0xA5 (1016 + 5).186: Would correspond roughly to 0xBA (1116 + 10).176: Would correspond to 0xB0 (1116 + 0).


Common Pitfalls:

Confusing A (10) with decimal 11 or 12.Dropping the contribution of the least significant digit.


Final Answer:

170

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