Solution - Base conversion

3, 546

3,546

Step-by-step explanation

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

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

${(D D A)}_{16} = 13 \cdot 16^{2} + 13 \cdot 16^{1} + 10 \cdot 16^{0}$

$13 \cdot 16^{2} + 13 \cdot 16^{1} + 10 \cdot 16^{0} = 3546$

Expand each digit by place value: $13 \cdot 16^{2}$
+ $13 \cdot 16^{1}$
+ $10 \cdot 16^{0}$ . This gives $3, 546$ in base 10.

$\frac{3546}{10} = 354 r e m a \in d e r 6$

$\frac{354}{10} = 35 r e m a \in d e r 4$

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

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

$6 \to 4 \to 5 \to 3 = 3546$

$3546 (b a s e 10) = {(3546)}_{10}$

Repeatedly divide $3, 546$ by $10$ , collect remainders, and read them in reverse to get $3, 546$ .

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