What is the 15's complement of the hexadecimal number (A10)16?
2016
What is the 15's complement of the hexadecimal number (A10)16?
Answer: A. (5EF)₁₆ — ConceptFor an n-digit hexadecimal number, the 15's complement is formed by replacing every digit d with F − d. Equivalently, it is the digit-wise subtraction…
- A.
(5EF)₁₆
- B.
(6F0)₁₆
- C.
(6FF)₁₆
- D.
(5E0)₁₆
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Correct answer: A
Concept
For an n-digit hexadecimal number, the 15's complement is formed by replacing every digit d with F − d.
Equivalently, it is the digit-wise subtraction of the number from an n-digit string of F symbols; no borrowing is needed when each position is handled separately.
Application
Use three F digits because (A10)16 has three hexadecimal digits: FFF.
Compute each position independently: F − A = 5, F − 1 = E, and F − 0 = F.
Write the resulting digits in the original order: (5EF)16.
Cross-check
Taking the 15's complement again gives F − 5 = A, F − E = 1, and F − F = 0, which reconstructs (A10)16.
Result
Therefore, the 15's complement is (5EF)16.