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

Difficulty: Easy

Correct Answer: 22

Explanation:


Introduction / Context:
Quick and accurate base conversion helps when reading datasheets, addresses, and register contents. The number 0x16 must be converted to decimal using the place-value method for base 16.

Given Data / Assumptions:

  • Hex digits: 1 and 6.
  • Positional weights: 16^1 and 16^0.
  • 16^1 = 16, 16^0 = 1.


Concept / Approach:
Multiply each digit by its positional weight and add the results. In hex, the leftmost digit has the higher power of 16 and the rightmost digit is multiplied by 1.

Step-by-Step Solution:

Compute high place: 1 * 16 = 16.Compute low place: 6 * 1 = 6.Sum: 16 + 6 = 22.


Verification / Alternative check:

Binary check: 0x16 = 0001 0110₂ = 16 + 4 + 2 = 22.


Why Other Options Are Wrong:

32: Would equal 0x20.25: Would be 0x19.27: Would be 0x1B.


Common Pitfalls:

Treating the hex digits as decimal places (1*10 + 6) which gives 16, not 22.Forgetting that hex includes digits A–F for values 10–15.


Final Answer:

22

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