Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?
Show Hint
- 15
- 21
- D2
- 528
The Correct Option is A
Solution and Explanation
Step 1: Convert the base-3 number to decimal.
The given number is $(210)_3$. Converting to decimal:
\[
(210)_3 = 2 \times 3^2 + 1 \times 3^1 + 0 \times 3^0 = 18 + 3 + 0 = 21
\]
Step 2: Convert the decimal number to hexadecimal.
Now convert $21_{10}$ to base 16:
\[
21_{10} = 1 \times 16 + 5
\]
So, the hexadecimal representation is $(15)_{16}$.
Step 3: Final conclusion.
Hence, the correct hexadecimal representation is 15.
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