Solution - Base conversion

1, 511

1,511

Step-by-step explanation

${(5 E 7)}_{16} = b a s e 10$

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

${(5 E 7)}_{16} = 5 \cdot 16^{2} + 14 \cdot 16^{1} + 7 \cdot 16^{0}$

$5 \cdot 16^{2} + 14 \cdot 16^{1} + 7 \cdot 16^{0} = 1511$

Expand each digit by place value: $5 \cdot 16^{2}$
+ $14 \cdot 16^{1}$
+ $7 \cdot 16^{0}$ . This gives $1, 511$ in base 10.

$\frac{1511}{10} = 151 r e m a \in d e r 1$

$\frac{151}{10} = 15 r e m a \in d e r 1$

$\frac{15}{10} = 1 r e m a \in d e r 5$

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

$1 \to 1 \to 5 \to 1 = 1511$

$1511 (b a s e 10) = {(1511)}_{10}$

Repeatedly divide $1, 511$ by $10$ , collect remainders, and read them in reverse to get $1, 511$ .

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