Solution - Base conversion

3, 293

3,293

Step-by-step explanation

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

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

${(C D D)}_{16} = 12 \cdot 16^{2} + 13 \cdot 16^{1} + 13 \cdot 16^{0}$

$12 \cdot 16^{2} + 13 \cdot 16^{1} + 13 \cdot 16^{0} = 3293$

Expand each digit by place value: $12 \cdot 16^{2}$
+ $13 \cdot 16^{1}$
+ $13 \cdot 16^{0}$ . This gives $3, 293$ in base 10.

$\frac{3293}{10} = 329 r e m a \in d e r 3$

$\frac{329}{10} = 32 r e m a \in d e r 9$

$\frac{32}{10} = 3 r e m a \in d e r 2$

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

$3 \to 9 \to 2 \to 3 = 3293$

$3293 (b a s e 10) = {(3293)}_{10}$

Repeatedly divide $3, 293$ by $10$ , collect remainders, and read them in reverse to get $3, 293$ .

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