Solution - Base conversion

932

932

Step-by-step explanation

${(3 A 4)}_{16} = b a s e 10$

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

${(3 A 4)}_{16} = 3 \cdot 16^{2} + 10 \cdot 16^{1} + 4 \cdot 16^{0}$

$3 \cdot 16^{2} + 10 \cdot 16^{1} + 4 \cdot 16^{0} = 932$

Expand each digit by place value: $3 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $4 \cdot 16^{0}$ . This gives $932$ in base 10.

$\frac{932}{10} = 93 r e m a \in d e r 2$

$\frac{93}{10} = 9 r e m a \in d e r 3$

$\frac{9}{10} = 0 r e m a \in d e r 9$

$2 \to 3 \to 9 = 932$

$932 (b a s e 10) = {(932)}_{10}$

Repeatedly divide $932$ by $10$ , collect remainders, and read them in reverse to get $932$ .

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