Solution - Base conversion

2, 986

2,986

Step-by-step explanation

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

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

${(B \forall)}_{16} = 11 \cdot 16^{2} + 10 \cdot 16^{1} + 10 \cdot 16^{0}$

$11 \cdot 16^{2} + 10 \cdot 16^{1} + 10 \cdot 16^{0} = 2986$

Expand each digit by place value: $11 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $10 \cdot 16^{0}$ . This gives $2, 986$ in base 10.

$\frac{2986}{10} = 298 r e m a \in d e r 6$

$\frac{298}{10} = 29 r e m a \in d e r 8$

$\frac{29}{10} = 2 r e m a \in d e r 9$

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

$6 \to 8 \to 9 \to 2 = 2986$

$2986 (b a s e 10) = {(2986)}_{10}$

Repeatedly divide $2, 986$ by $10$ , collect remainders, and read them in reverse to get $2, 986$ .

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