Solution - Base conversion

174

174

Step-by-step explanation

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

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

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

$10 \cdot 16^{1} + 14 \cdot 16^{0} = 174$

Expand each digit by place value: $10 \cdot 16^{1}$
+ $14 \cdot 16^{0}$ . This gives $174$ in base 10.

$\frac{174}{10} = 17 r e m a \in d e r 4$

$\frac{17}{10} = 1 r e m a \in d e r 7$

$\frac{1}{10} = 0 r e m a \in d e r 1$

$4 \to 7 \to 1 = 174$

$174 (b a s e 10) = {(174)}_{10}$

Repeatedly divide $174$ by $10$ , collect remainders, and read them in reverse to get $174$ .

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