Solution - Base conversion

219

219

Step-by-step explanation

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

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

${(D B)}_{16} = 13 \cdot 16^{1} + 11 \cdot 16^{0}$

$13 \cdot 16^{1} + 11 \cdot 16^{0} = 219$

Expand each digit by place value: $13 \cdot 16^{1}$
+ $11 \cdot 16^{0}$ . This gives $219$ in base 10.

$\frac{219}{10} = 21 r e m a \in d e r 9$

$\frac{21}{10} = 2 r e m a \in d e r 1$

$\frac{2}{10} = 0 r e m a \in d e r 2$

$9 \to 1 \to 2 = 219$

$219 (b a s e 10) = {(219)}_{10}$

Repeatedly divide $219$ by $10$ , collect remainders, and read them in reverse to get $219$ .

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