Solution - Base conversion

3, 322

3,322

Step-by-step explanation

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

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

${(C F A)}_{16} = 12 \cdot 16^{2} + 15 \cdot 16^{1} + 10 \cdot 16^{0}$

$12 \cdot 16^{2} + 15 \cdot 16^{1} + 10 \cdot 16^{0} = 3322$

Expand each digit by place value: $12 \cdot 16^{2}$
+ $15 \cdot 16^{1}$
+ $10 \cdot 16^{0}$ . This gives $3, 322$ in base 10.

$\frac{3322}{10} = 332 r e m a \in d e r 2$

$\frac{332}{10} = 33 r e m a \in d e r 2$

$\frac{33}{10} = 3 r e m a \in d e r 3$

$\frac{3}{10} = 0 r e m a \in d e r 3$

$2 \to 2 \to 3 \to 3 = 3322$

$3322 (b a s e 10) = {(3322)}_{10}$

Repeatedly divide $3, 322$ by $10$ , collect remainders, and read them in reverse to get $3, 322$ .

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