Solution - Base conversion

2, 530

2,530

Step-by-step explanation

${(9 E 2)}_{16} = b a s e 10$

Identify the source number, source base, and target base before converting through base 10.

${(9 E 2)}_{16} = 9 \cdot 16^{2} + 14 \cdot 16^{1} + 2 \cdot 16^{0}$

$9 \cdot 16^{2} + 14 \cdot 16^{1} + 2 \cdot 16^{0} = 2530$

Expand each digit by place value: $9 \cdot 16^{2}$
+ $14 \cdot 16^{1}$
+ $2 \cdot 16^{0}$ . This gives $2, 530$ in base 10.

$\frac{2530}{10} = 253 r e m a \in d e r 0$

$\frac{253}{10} = 25 r e m a \in d e r 3$

$\frac{25}{10} = 2 r e m a \in d e r 5$

$\frac{2}{10} = 0 r e m a \in d e r 2$

$0 \to 3 \to 5 \to 2 = 2530$

$2530 (b a s e 10) = {(2530)}_{10}$

Repeatedly divide $2, 530$ by $10$ , collect remainders, and read them in reverse to get $2, 530$ .

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Base conversion is foundational for computer science, digital systems, and number theory.