Solution - Base conversion

4, 014

4,014

Step-by-step explanation

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

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

${(F A E)}_{16} = 15 \cdot 16^{2} + 10 \cdot 16^{1} + 14 \cdot 16^{0}$

$15 \cdot 16^{2} + 10 \cdot 16^{1} + 14 \cdot 16^{0} = 4014$

Expand each digit by place value: $15 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $14 \cdot 16^{0}$ . This gives $4, 014$ in base 10.

$\frac{4014}{10} = 401 r e m a \in d e r 4$

$\frac{401}{10} = 40 r e m a \in d e r 1$

$\frac{40}{10} = 4 r e m a \in d e r 0$

$\frac{4}{10} = 0 r e m a \in d e r 4$

$4 \to 1 \to 0 \to 4 = 4014$

$4014 (b a s e 10) = {(4014)}_{10}$

Repeatedly divide $4, 014$ by $10$ , collect remainders, and read them in reverse to get $4, 014$ .

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