Solution - Base conversion

423

423

Step-by-step explanation

${(1 A 7)}_{16} = b a s e 10$

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

${(1 A 7)}_{16} = 1 \cdot 16^{2} + 10 \cdot 16^{1} + 7 \cdot 16^{0}$

$1 \cdot 16^{2} + 10 \cdot 16^{1} + 7 \cdot 16^{0} = 423$

Expand each digit by place value: $1 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $7 \cdot 16^{0}$ . This gives $423$ in base 10.

$\frac{423}{10} = 42 r e m a \in d e r 3$

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

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

$3 \to 2 \to 4 = 423$

$423 (b a s e 10) = {(423)}_{10}$

Repeatedly divide $423$ by $10$ , collect remainders, and read them in reverse to get $423$ .

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