GATE CS 2021 Set 1 Q6 — Number Representations (Fixed and Floating Point)

To find the hexadecimal representation of the number $(210)_3$, we first convert it to its decimal (base-10) equivalent and then convert that decimal value to hexadecimal (base-16).

Step 1: Convert $(210)_3$ to decimal

$$(210)_3 = 2 \times 3^2 + 1 \times 3^1 + 0 \times 3^0$$ $$= 2 \times 9 + 1 \times 3 + 0$$ $$= 18 + 3 = 21_{10}$$

Step 2: Convert $21_{10}$ to hexadecimal

We divide the decimal number by $16$ and record the remainders:

• $21 \div 16 = 1$ with a remainder of $5$
• $1 \div 16 = 0$ with a remainder of $1$

Thus, the hexadecimal representation of the number is $15$, which corresponds to option A.