Solution - Base conversion

2, 766

2,766

Step-by-step explanation

${(A C E)}_{16} = b a s e 10$

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

${(A C E)}_{16} = 10 \cdot 16^{2} + 12 \cdot 16^{1} + 14 \cdot 16^{0}$

$10 \cdot 16^{2} + 12 \cdot 16^{1} + 14 \cdot 16^{0} = 2766$

Expand each digit by place value: $10 \cdot 16^{2}$
+ $12 \cdot 16^{1}$
+ $14 \cdot 16^{0}$ . This gives $2, 766$ in base 10.

$\frac{2766}{10} = 276 r e m a \in d e r 6$

$\frac{276}{10} = 27 r e m a \in d e r 6$

$\frac{27}{10} = 2 r e m a \in d e r 7$

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

$6 \to 6 \to 7 \to 2 = 2766$

$2766 (b a s e 10) = {(2766)}_{10}$

Repeatedly divide $2, 766$ by $10$ , collect remainders, and read them in reverse to get $2, 766$ .

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