Solution - Base conversion

2, 217

2,217

Step-by-step explanation

${(8 A 9)}_{16} = b a s e 10$

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

${(8 A 9)}_{16} = 8 \cdot 16^{2} + 10 \cdot 16^{1} + 9 \cdot 16^{0}$

$8 \cdot 16^{2} + 10 \cdot 16^{1} + 9 \cdot 16^{0} = 2217$

Expand each digit by place value: $8 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $9 \cdot 16^{0}$ . This gives $2, 217$ in base 10.

$\frac{2217}{10} = 221 r e m a \in d e r 7$

$\frac{221}{10} = 22 r e m a \in d e r 1$

$\frac{22}{10} = 2 r e m a \in d e r 2$

$\frac{2}{10} = 0 r e m a \in d e r 2$

$7 \to 1 \to 2 \to 2 = 2217$

$2217 (b a s e 10) = {(2217)}_{10}$

Repeatedly divide $2, 217$ by $10$ , collect remainders, and read them in reverse to get $2, 217$ .

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