Solution - Base conversion

2, 007

2,007

Step-by-step explanation

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

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

${(7 D 7)}_{16} = 7 \cdot 16^{2} + 13 \cdot 16^{1} + 7 \cdot 16^{0}$

$7 \cdot 16^{2} + 13 \cdot 16^{1} + 7 \cdot 16^{0} = 2007$

Expand each digit by place value: $7 \cdot 16^{2}$
+ $13 \cdot 16^{1}$
+ $7 \cdot 16^{0}$ . This gives $2, 007$ in base 10.

$\frac{2007}{10} = 200 r e m a \in d e r 7$

$\frac{200}{10} = 20 r e m a \in d e r 0$

$\frac{20}{10} = 2 r e m a \in d e r 0$

$\frac{2}{10} = 0 r e m a \in d e r 2$

$7 \to 0 \to 0 \to 2 = 2007$

$2007 (b a s e 10) = {(2007)}_{10}$

Repeatedly divide $2, 007$ by $10$ , collect remainders, and read them in reverse to get $2, 007$ .

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