Solution - Base conversion

4, 091

4,091

Step-by-step explanation

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

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

${(F F B)}_{16} = 15 \cdot 16^{2} + 15 \cdot 16^{1} + 11 \cdot 16^{0}$

$15 \cdot 16^{2} + 15 \cdot 16^{1} + 11 \cdot 16^{0} = 4091$

Expand each digit by place value: $15 \cdot 16^{2}$
+ $15 \cdot 16^{1}$
+ $11 \cdot 16^{0}$ . This gives $4, 091$ in base 10.

$\frac{4091}{10} = 409 r e m a \in d e r 1$

$\frac{409}{10} = 40 r e m a \in d e r 9$

$\frac{40}{10} = 4 r e m a \in d e r 0$

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

$1 \to 9 \to 0 \to 4 = 4091$

$4091 (b a s e 10) = {(4091)}_{10}$

Repeatedly divide $4, 091$ by $10$ , collect remainders, and read them in reverse to get $4, 091$ .

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