Solution - Base conversion

3, 052

3,052

Step-by-step explanation

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

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

${(B E C)}_{16} = 11 \cdot 16^{2} + 14 \cdot 16^{1} + 12 \cdot 16^{0}$

$11 \cdot 16^{2} + 14 \cdot 16^{1} + 12 \cdot 16^{0} = 3052$

Expand each digit by place value: $11 \cdot 16^{2}$
+ $14 \cdot 16^{1}$
+ $12 \cdot 16^{0}$ . This gives $3, 052$ in base 10.

$\frac{3052}{10} = 305 r e m a \in d e r 2$

$\frac{305}{10} = 30 r e m a \in d e r 5$

$\frac{30}{10} = 3 r e m a \in d e r 0$

$\frac{3}{10} = 0 r e m a \in d e r 3$

$2 \to 5 \to 0 \to 3 = 3052$

$3052 (b a s e 10) = {(3052)}_{10}$

Repeatedly divide $3, 052$ by $10$ , collect remainders, and read them in reverse to get $3, 052$ .

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