Solution - Base conversion

728

728

Step-by-step explanation

${(2 D 8)}_{16} = b a s e 10$

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

${(2 D 8)}_{16} = 2 \cdot 16^{2} + 13 \cdot 16^{1} + 8 \cdot 16^{0}$

$2 \cdot 16^{2} + 13 \cdot 16^{1} + 8 \cdot 16^{0} = 728$

Expand each digit by place value: $2 \cdot 16^{2}$
+ $13 \cdot 16^{1}$
+ $8 \cdot 16^{0}$ . This gives $728$ in base 10.

$\frac{728}{10} = 72 r e m a \in d e r 8$

$\frac{72}{10} = 7 r e m a \in d e r 2$

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

$8 \to 2 \to 7 = 728$

$728 (b a s e 10) = {(728)}_{10}$

Repeatedly divide $728$ by $10$ , collect remainders, and read them in reverse to get $728$ .

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