Solution - Base conversion

2, 514

2,514

Step-by-step explanation

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

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

${(9 D 2)}_{16} = 9 \cdot 16^{2} + 13 \cdot 16^{1} + 2 \cdot 16^{0}$

$9 \cdot 16^{2} + 13 \cdot 16^{1} + 2 \cdot 16^{0} = 2514$

Expand each digit by place value: $9 \cdot 16^{2}$
+ $13 \cdot 16^{1}$
+ $2 \cdot 16^{0}$ . This gives $2, 514$ in base 10.

$\frac{2514}{10} = 251 r e m a \in d e r 4$

$\frac{251}{10} = 25 r e m a \in d e r 1$

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

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

$4 \to 1 \to 5 \to 2 = 2514$

$2514 (b a s e 10) = {(2514)}_{10}$

Repeatedly divide $2, 514$ by $10$ , collect remainders, and read them in reverse to get $2, 514$ .

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