Solution - Base conversion

488

488

Step-by-step explanation

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

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

${(1 E 8)}_{16} = 1 \cdot 16^{2} + 14 \cdot 16^{1} + 8 \cdot 16^{0}$

$1 \cdot 16^{2} + 14 \cdot 16^{1} + 8 \cdot 16^{0} = 488$

Expand each digit by place value: $1 \cdot 16^{2}$
+ $14 \cdot 16^{1}$
+ $8 \cdot 16^{0}$ . This gives $488$ in base 10.

$\frac{488}{10} = 48 r e m a \in d e r 8$

$\frac{48}{10} = 4 r e m a \in d e r 8$

$\frac{4}{10} = 0 r e m a \in d e r 4$

$8 \to 8 \to 4 = 488$

$488 (b a s e 10) = {(488)}_{10}$

Repeatedly divide $488$ by $10$ , collect remainders, and read them in reverse to get $488$ .

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