Solution - Base conversion

1, 237

1,237

Step-by-step explanation

${(4 D 5)}_{16} = b a s e 10$

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

${(4 D 5)}_{16} = 4 \cdot 16^{2} + 13 \cdot 16^{1} + 5 \cdot 16^{0}$

$4 \cdot 16^{2} + 13 \cdot 16^{1} + 5 \cdot 16^{0} = 1237$

Expand each digit by place value: $4 \cdot 16^{2}$
+ $13 \cdot 16^{1}$
+ $5 \cdot 16^{0}$ . This gives $1, 237$ in base 10.

$\frac{1237}{10} = 123 r e m a \in d e r 7$

$\frac{123}{10} = 12 r e m a \in d e r 3$

$\frac{12}{10} = 1 r e m a \in d e r 2$

$\frac{1}{10} = 0 r e m a \in d e r 1$

$7 \to 3 \to 2 \to 1 = 1237$

$1237 (b a s e 10) = {(1237)}_{10}$

Repeatedly divide $1, 237$ by $10$ , collect remainders, and read them in reverse to get $1, 237$ .

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