Solution - Base conversion

2, 505

2,505

Step-by-step explanation

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

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

${(9 C 9)}_{16} = 9 \cdot 16^{2} + 12 \cdot 16^{1} + 9 \cdot 16^{0}$

$9 \cdot 16^{2} + 12 \cdot 16^{1} + 9 \cdot 16^{0} = 2505$

Expand each digit by place value: $9 \cdot 16^{2}$
+ $12 \cdot 16^{1}$
+ $9 \cdot 16^{0}$ . This gives $2, 505$ in base 10.

$\frac{2505}{10} = 250 r e m a \in d e r 5$

$\frac{250}{10} = 25 r e m a \in d e r 0$

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

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

$5 \to 0 \to 5 \to 2 = 2505$

$2505 (b a s e 10) = {(2505)}_{10}$

Repeatedly divide $2, 505$ by $10$ , collect remainders, and read them in reverse to get $2, 505$ .

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