Solution - Base conversion

504

504

Step-by-step explanation

${(1 F 8)}_{16} = b a s e 10$

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

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

$1 \cdot 16^{2} + 15 \cdot 16^{1} + 8 \cdot 16^{0} = 504$

Expand each digit by place value: $1 \cdot 16^{2}$
+ $15 \cdot 16^{1}$
+ $8 \cdot 16^{0}$ . This gives $504$ in base 10.

$\frac{504}{10} = 50 r e m a \in d e r 4$

$\frac{50}{10} = 5 r e m a \in d e r 0$

$\frac{5}{10} = 0 r e m a \in d e r 5$

$4 \to 0 \to 5 = 504$

$504 (b a s e 10) = {(504)}_{10}$

Repeatedly divide $504$ by $10$ , collect remainders, and read them in reverse to get $504$ .

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