Solution - Base conversion

705

705

Step-by-step explanation

${(2 C 1)}_{16} = b a s e 10$

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

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

$2 \cdot 16^{2} + 12 \cdot 16^{1} + 1 \cdot 16^{0} = 705$

Expand each digit by place value: $2 \cdot 16^{2}$
+ $12 \cdot 16^{1}$
+ $1 \cdot 16^{0}$ . This gives $705$ in base 10.

$\frac{705}{10} = 70 r e m a \in d e r 5$

$\frac{70}{10} = 7 r e m a \in d e r 0$

$\frac{7}{10} = 0 r e m a \in d e r 7$

$5 \to 0 \to 7 = 705$

$705 (b a s e 10) = {(705)}_{10}$

Repeatedly divide $705$ by $10$ , collect remainders, and read them in reverse to get $705$ .

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