Base conversion — Convert the hexadecimal number 16 (base 16) to its decimal (base 10) value.
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
-
A32
-
B22
-
C25
-
D27
Answer
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