Solution - Base conversion

3, 567

3,567

Step-by-step explanation

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

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

${(D E F)}_{16} = 13 \cdot 16^{2} + 14 \cdot 16^{1} + 15 \cdot 16^{0}$

$13 \cdot 16^{2} + 14 \cdot 16^{1} + 15 \cdot 16^{0} = 3567$

Expand each digit by place value: $13 \cdot 16^{2}$
+ $14 \cdot 16^{1}$
+ $15 \cdot 16^{0}$ . This gives $3, 567$ in base 10.

$\frac{3567}{10} = 356 r e m a \in d e r 7$

$\frac{356}{10} = 35 r e m a \in d e r 6$

$\frac{35}{10} = 3 r e m a \in d e r 5$

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

$7 \to 6 \to 5 \to 3 = 3567$

$3567 (b a s e 10) = {(3567)}_{10}$

Repeatedly divide $3, 567$ by $10$ , collect remainders, and read them in reverse to get $3, 567$ .

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