GATE CS Mastery
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GATE CS 2021 Set 1 · Digital Logic

Question 16

MCQPrinted as CS Q.61 markWrong answer: −1/3Easy (estimate)

Question

Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

Choose one option
Official answer and solution
Official answer
A
From
Official GATE 2021 answer key

Solution

Convert the base-3 number to decimal, then convert the decimal value to hexadecimal.

The number is (210)3(210)_3. Expanding in base 10:

(210)3=2×32+1×31+0×30=2×9+3+0=2110(210)_3 = 2 \times 3^2 + 1 \times 3^1 + 0 \times 3^0 = 2 \times 9 + 3 + 0 = 21_{10}

Now convert 211021_{10} to hexadecimal (base 16):

21=1×161+5×160=(15)1621 = 1 \times 16^1 + 5 \times 16^0 = (15)_{16}

Therefore, the hexadecimal representation is 15, matching option A.

Final answer

A

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2021 Computer Science and Information Technology (CS, Set-1)
Question
16 of 65, printed as CS Q.6
Section
Computer Science and Information Technology

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