Solution - Base conversion

3, 037

3,037

Step-by-step explanation

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

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

${(B D D)}_{16} = 11 \cdot 16^{2} + 13 \cdot 16^{1} + 13 \cdot 16^{0}$

$11 \cdot 16^{2} + 13 \cdot 16^{1} + 13 \cdot 16^{0} = 3037$

Expand each digit by place value: $11 \cdot 16^{2}$
+ $13 \cdot 16^{1}$
+ $13 \cdot 16^{0}$ . This gives $3, 037$ in base 10.

$\frac{3037}{10} = 303 r e m a \in d e r 7$

$\frac{303}{10} = 30 r e m a \in d e r 3$

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

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

$7 \to 3 \to 0 \to 3 = 3037$

$3037 (b a s e 10) = {(3037)}_{10}$

Repeatedly divide $3, 037$ by $10$ , collect remainders, and read them in reverse to get $3, 037$ .

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