Solution - Base conversion

448

448

Step-by-step explanation

${(1 C 0)}_{16} = b a s e 10$

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

${(1 C 0)}_{16} = 1 \cdot 16^{2} + 12 \cdot 16^{1} + 0 \cdot 16^{0}$

$1 \cdot 16^{2} + 12 \cdot 16^{1} + 0 \cdot 16^{0} = 448$

Expand each digit by place value: $1 \cdot 16^{2}$
+ $12 \cdot 16^{1}$
+ $0 \cdot 16^{0}$ . This gives $448$ in base 10.

$\frac{448}{10} = 44 r e m a \in d e r 8$

$\frac{44}{10} = 4 r e m a \in d e r 4$

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

$8 \to 4 \to 4 = 448$

$448 (b a s e 10) = {(448)}_{10}$

Repeatedly divide $448$ by $10$ , collect remainders, and read them in reverse to get $448$ .

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