Solution - Base conversion

676

676

Step-by-step explanation

${(2 A 4)}_{16} = b a s e 10$

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

${(2 A 4)}_{16} = 2 \cdot 16^{2} + 10 \cdot 16^{1} + 4 \cdot 16^{0}$

$2 \cdot 16^{2} + 10 \cdot 16^{1} + 4 \cdot 16^{0} = 676$

Expand each digit by place value: $2 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $4 \cdot 16^{0}$ . This gives $676$ in base 10.

$\frac{676}{10} = 67 r e m a \in d e r 6$

$\frac{67}{10} = 6 r e m a \in d e r 7$

$\frac{6}{10} = 0 r e m a \in d e r 6$

$6 \to 7 \to 6 = 676$

$676 (b a s e 10) = {(676)}_{10}$

Repeatedly divide $676$ by $10$ , collect remainders, and read them in reverse to get $676$ .

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