Solution - Base conversion

1, 016

1,016

Step-by-step explanation

${(3 F 8)}_{16} = b a s e 10$

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

${(3 F 8)}_{16} = 3 \cdot 16^{2} + 15 \cdot 16^{1} + 8 \cdot 16^{0}$

$3 \cdot 16^{2} + 15 \cdot 16^{1} + 8 \cdot 16^{0} = 1016$

Expand each digit by place value: $3 \cdot 16^{2}$
+ $15 \cdot 16^{1}$
+ $8 \cdot 16^{0}$ . This gives $1, 016$ in base 10.

$\frac{1016}{10} = 101 r e m a \in d e r 6$

$\frac{101}{10} = 10 r e m a \in d e r 1$

$\frac{10}{10} = 1 r e m a \in d e r 0$

$\frac{1}{10} = 0 r e m a \in d e r 1$

$6 \to 1 \to 0 \to 1 = 1016$

$1016 (b a s e 10) = {(1016)}_{10}$

Repeatedly divide $1, 016$ by $10$ , collect remainders, and read them in reverse to get $1, 016$ .

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