Solution - Base conversion

997

997

Step-by-step explanation

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

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

${(3 E 5)}_{16} = 3 \cdot 16^{2} + 14 \cdot 16^{1} + 5 \cdot 16^{0}$

$3 \cdot 16^{2} + 14 \cdot 16^{1} + 5 \cdot 16^{0} = 997$

Expand each digit by place value: $3 \cdot 16^{2}$
+ $14 \cdot 16^{1}$
+ $5 \cdot 16^{0}$ . This gives $997$ in base 10.

$\frac{997}{10} = 99 r e m a \in d e r 7$

$\frac{99}{10} = 9 r e m a \in d e r 9$

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

$7 \to 9 \to 9 = 997$

$997 (b a s e 10) = {(997)}_{10}$

Repeatedly divide $997$ by $10$ , collect remainders, and read them in reverse to get $997$ .

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