Solution - Base conversion

422

422

Step-by-step explanation

${(1 A 6)}_{16} = b a s e 10$

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

${(1 A 6)}_{16} = 1 \cdot 16^{2} + 10 \cdot 16^{1} + 6 \cdot 16^{0}$

$1 \cdot 16^{2} + 10 \cdot 16^{1} + 6 \cdot 16^{0} = 422$

Expand each digit by place value: $1 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $6 \cdot 16^{0}$ . This gives $422$ in base 10.

$\frac{422}{10} = 42 r e m a \in d e r 2$

$\frac{42}{10} = 4 r e m a \in d e r 2$

$\frac{4}{10} = 0 r e m a \in d e r 4$

$2 \to 2 \to 4 = 422$

$422 (b a s e 10) = {(422)}_{10}$

Repeatedly divide $422$ by $10$ , collect remainders, and read them in reverse to get $422$ .

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