Solution - Base conversion

981

981

Step-by-step explanation

${(3 D 5)}_{16} = b a s e 10$

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

${(3 D 5)}_{16} = 3 \cdot 16^{2} + 13 \cdot 16^{1} + 5 \cdot 16^{0}$

$3 \cdot 16^{2} + 13 \cdot 16^{1} + 5 \cdot 16^{0} = 981$

Expand each digit by place value: $3 \cdot 16^{2}$
+ $13 \cdot 16^{1}$
+ $5 \cdot 16^{0}$ . This gives $981$ in base 10.

$\frac{981}{10} = 98 r e m a \in d e r 1$

$\frac{98}{10} = 9 r e m a \in d e r 8$

$\frac{9}{10} = 0 r e m a \in d e r 9$

$1 \to 8 \to 9 = 981$

$981 (b a s e 10) = {(981)}_{10}$

Repeatedly divide $981$ by $10$ , collect remainders, and read them in reverse to get $981$ .

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