Solution - Base conversion

2, 039

2,039

Step-by-step explanation

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

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

${(7 F 7)}_{16} = 7 \cdot 16^{2} + 15 \cdot 16^{1} + 7 \cdot 16^{0}$

$7 \cdot 16^{2} + 15 \cdot 16^{1} + 7 \cdot 16^{0} = 2039$

Expand each digit by place value: $7 \cdot 16^{2}$
+ $15 \cdot 16^{1}$
+ $7 \cdot 16^{0}$ . This gives $2, 039$ in base 10.

$\frac{2039}{10} = 203 r e m a \in d e r 9$

$\frac{203}{10} = 20 r e m a \in d e r 3$

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

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

$9 \to 3 \to 0 \to 2 = 2039$

$2039 (b a s e 10) = {(2039)}_{10}$

Repeatedly divide $2, 039$ by $10$ , collect remainders, and read them in reverse to get $2, 039$ .

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